partial classification of modules for the algebra of skew derivations over the d dimensional torus for the algebra of skew derivations over a torus we classify the irreducible weight modules with some restrictions

approximations of temporal rainfall from a multidimensional model the feasibility of representing the temporal structure of a multidimensional rainfall process with simpler stochastic models and a study of the effect of parameter robustness on the time scale is investigated here via performing controlled numerical experiments a multidimensional representation for precipitation given in the theory recently proposed by e waymire et al 1984 is used for simulating rainfall in space and time the model produces moving storms with realistic mesoscale meteorological features e g clustering birth and death of cells cell intensity attenuation in time and space etc two year traces of rainfall intensities at fixed gage stations were generated at intervals of 0 1 hours for three climates these traces are then aggregated at different time scales ranging from 1 to 24 hours first and second order statistics are evaluated from the above series at each aggregation level and they are used for estimating the parameters of three one dimensional models of temporal rainfall at a point 1 poisson model with independent marks 2 rectangular pulses with independent intensity and duration and 3 neyman scott with independent marks only at very high levels of aggregation the compound poisson model was able to reproduce the statistical structure of the simulated traces the rectangular pulses model was found to have parameters which vary significantly with the time scale of aggregation and moreover it leads to large distortions in the mean depth and duration of storm events the neyman scott scheme proved to be the most stable model throughout the different time scales and it also reproduced quite well the average storm characteristics at the event level none of these three models was able to reproduce in a satisfactory manner the simulated extreme value distribution of the multidimensional model

integrable representations of toroidal lie algebras co ordinatized by rational quantum tori for any positive integers d n with d 1 and n 1 we fix an n by n complex matrix q qij satisfying qii 1 and qij qji 1 with all qij roots of unity let d q be the universal central extension of the lie subalgebra sld cq of gld cq with trace in cq cq where cq is the rational quantum torus associated to q and let d q be the lie algebra by adding the n degree derivations to d q with respect to the n non commuting variables in cq the lie algebra d q called the toroidal lie algebra co ordinatized by the rational quantum torus cq has an n dimensional center c in this paper we obtain a classification of irreducible integrable modules with finite dimensional weight spaces and with non zero center action over the toroidal lie algebra d q

modules of highest weight type for the algebra of derivations over a rational quantum torus for the lie algebra of derivations over a rational quantum torus we construct a class of irreducible weight modules with all finite dimensional weight spaces which are called the modules of highest weight type generating the notion for the case of commutative torus for the lie algebra of derivations over a rational quantum torus we construct a class of irreducible weight modules with all finite dimensional weight spaces which are called the modules of highest weight type generating the notion for the case of commutative torus

two parameter quantum affine algebra of type g2 1 drinfeld realization and vertex representation in this paper we define the two parameter quantum affine algebra for type g2 1 and give the r s drinfeld realization of ur s g2 1 as well as establish and prove its drinfeld isomorphism we construct and verify explicitly the level one vertex representation of two parameter quantum affine algebra ur s g2 1 which also supports an evidence in nontwisted type g2 1 for the uniform defining approach via the two parameter invariant generating functions proposed in hu and zhang generating functions with invariance and vertex representations of two parameter quantum affine algebras ur s g simply laced cases e print arxiv 1401 4925

multidimensional modeling of cumulative rainfall parameter estimation and model adequacy through a continuum of scales this paper presents the multidimensional representation of the cumulative rainfall process and derives a closed form expression for the mean and space time covariance functions a parameter estimation procedure is developed sensitivity analysis provides useful information for devising the parameter estimation strategy the cumulative rainfall model is applied to 8 years of digitized rain gage data from the walnut gulch experimental watershed the most useful feature of the model is its self consistency implying that even after using information from a given limited set of data it still leads to realistic parameters which reproduce historical statistics at several levels of time and space scales

lie algebras graded by finite root systems and intersection matrix algebras this paper classifies the lie algebras graded by doubly laced finite root systems and applies this classification to identify the intersection matrix algebras arising from multiply affinized cartan matrices of types b c f and g this completes the determination of the lie algebras graded by finite root systems initiated by berman and moody who studied the simply laced finite root systems of rank 2

stochastic modeling of multidimensional precipitation fields considering spectral structure a multidimensional stochastic precipitation model with major emphasis on its spectral structure is proposed as a hyperbolic type of stochastic partial differential equation this model is characterized by a small set of easily estimable parameters these characteristics are similar to those of the noise forced diffusive precipitation model but the representation of the physical and statistical features of the precipitation field is similar to that of the waymire gupta rodriguez iturbe wgr precipitation model the derivation was based on the autoregressive process considering advection and diffusion the dominant statistical and physical characteristics of the precipitation field propagation the model spectrum showed a good match with the global atlantic tropical experiment spectrum this model was also compared with the wgr model and the noise forced diffusive precipitation model both analytically and through applications such as the sampling error estimation from spaceborne sensors and rain gauges the sampling error from spaceborne sensors based on the proposed model was similar to that of the noise forced diffusive precipitation model but much smaller than that of the wgr model similar results were also obtained in the estimation of the sampling error from rain gauges

on the bcjr algorithm for rate distortion source coding the bahl cocke jelinek raviv bcjr algorithm is an important channel decoding method we extend it to trellis rate distortion data compression beginning from source coding principles the derivation of the algorithm avoids channel coding or soft output ideas the encoder does not use entropy coding equiprobable reproducer letters are emphasized since these maximize entropy the bcjr method is demonstrated by tests of a tail biting variant it performs much better than the ordinary viterbi algorithm for short and medium blocks however the improvement stems from tail biting the role of the bcjr is to achieve tail biting in a relatively simple way some issues that arise with tail biting are explored it is shown that there is an optimal trellis state size for each block length

central and noncentral extensions of multi graded lie algebras the author constructs noncentral extensions of the algebras of vector fields and gauge transformations in n dimensional space in one dimension they reduce to the ordinary central extensions occurring in virasoro and kac moody algebras

integrable representations for generalized virasoro toroidal lie algebras abstract in this paper we give the structure of irreducible integrable modules of generalized virasoro toroidal lie algebras with finite dimensional weight spaces and non zero central charge

lowest energy representations of non centrally extended diffeomorphism algebras we describe a class of non central extensions of the diffeomorphism algebra in n dimensional spacetime and construct lowest energy modules thereof thus generalizing work of eswara rao and moody there is one representation for each representation of an extension of the semi direct product similar modules are constructed for gauge algebras

differential equations in vertex algebras and simple modules for the lie algebra of vector fields on a torus we study irreducible representations for the lie algebra of vector fields on a 2 dimensional torus constructed using the generalized verma modules we show that for a certain choice of parameters these representations remain irreducible when restricted to a loop subalgebra in the lie algebra of vector fields we prove this result by studying vertex algebras associated with the lie algebra of vector fields on a torus and solving non commutative differential equations that we derive using the vertex algebra technique

classification of irreducible integrable modules for toroidal lie algebras with finite dimensional weight spaces the purpose of this paper is to classify irreducible integrable modules for multi loop algebras let v be a vector space over the complex numbers let a t 1 t n be the laurent polynomials ring in n variables let va v a and let v m v t for m m1 mn n and t t1 1 t2 2 tn n let be a simple finite dimensional lie algebra over the complex numbers then a can be given a lie algebra structure see 1 1 let d1 dn be derivations defined by di x m mix m and let d be the linear span of d1 dn then a a is a lie algebra which we call a multi loop algebra the universal central externion of a is called a toroidal lie algebra and is studied in bb bc e3 e4 em so our multiloop algebras are quotients of toroidal lie algebras by centers fix a cartan subalgebra h of let be a graded homomorphism of u ha a see section 1 for details then we can define the universal highest weight module m for a let v be the unique irreducible quotient of m we then prove in theorem 3 4 that any irreducible integrable module for a is isomorphic to v by making use of a result from chari c we associate to a map from u ha by evaluating at 1 and an irreducible module v for a derivations do not act on v and therefore it cannot be extended to a now consider v a as a

principal vertex operator representations for toroidal lie algebras we introduce the principal vertex operator representations for the toroidal lie algebras generalizing the construction for the affine kac moody algebras we also represent the derivations of the toroidal algebras and introduce analogs of the sugawara operators

a new family of algebras underlying the rogers ramanujan identities and generalizations abstract the classical rogers ramanujan identities have been interpreted by lepowsky milne and the present authors in terms of the representation theory of the euclidean kac moody lie algebra a1 1 also the present authors have introduced certain vertex differential operators providing a construction of a1 1 on its basic module and kac kazhdan and we have generalized this construction to a general class of euclidean lie algebras starting from this viewpoint we now introduce certain new algebras unk v which centralize the action of the principal heisenberg subalgebra of an arbitrary euclidean lie algebra unk on a highest weight unk module v we state a general tautological rogers ramanujan type identity which by our earlier theorem includes the classical identities and we show that unk v can be used to reformulate the general identity for unk a1 1 we develop the representation theory of unk v in considerable detail allowing us to prove our earlier conjecture that our general rogers ramanujan type identity includes certain identities of gordon andrews and bressoud in the process we construct explicit bases of all of the standard and verma modules of nonzero level for a1 1 with an explicit realization of a1 1 as operators in each case the differential operator constructions mentioned above correspond to the trivial case unk v 1 of the present theory

a class of integrable modules for the core of eala coordinatized by quantum tori extended affine lie algebras eala are higher dimensional generalizations of affine kac moody lie algebras introduced in 19 they have been further studied in 1 2 5 toroidal lie algebras which are universal central extensions of g c t 1 1 t 1 n g simple finite dimensional lie algebra and are prime examples of cores of ealas which are studied in 4 7 14 16 22 24 25 there are many ealas which allow not only laurent polynomial algebra c t 1 1 t 1 n as co ordinate algebra but also quantum tori jordan tori and the octonians tori as co ordinated algebras depending on type of the lie algebra see 1 3 5 6 26 the structure theory of the eala of type ad 1 is tied up with lie algebra gld c cq where cq is the quantum torus see section 1 quantum tori defined in 21 are non commutative analogue of laurent polynomial algebras in this paper we study integrable modules for the core of the eala corresponding to gld c cq which we call we will also add derivations d1 d2 to and call it here cq is two variable quantum torus defined as the ring of non commutating laurent polynomials c t 1 1 t 1 2 with relation to t1t2 qt2t1 note that if q is generic then is an eala we classify theorem 5 2 irreducible integrable modules see definition 1 9 for where the zero degree center acts non trivially we prove that any such module is isomorphic to a highest weight module or a lowest module up to an automorphism see section 5 let and aff be finite and affine root system of sld c and its affinization consider aff z 2 and consider the subalgebra b corresponding to see section 1 by highest weight modules we mean a module with a weight vector killed by b and the highest weight h c t t 1 given as in theorem 4 1 for any such we define a highest weight module

optimal and near optimal encoders for short and moderate length tail biting trellises the results of an extensive search for short and moderate length polynomial convolutional encoders for time invariant tail biting representations of block codes at rates r 1 4 1 3 1 2 and 2 3 are reported the tail biting representations found are typically as good as the best known block codes

some categories of modules for toroidal lie algebras nsf of china 10931006 11371024 phd programs foundation of ministry of education of china 20100121110014 natural science foundation of fujian province 2013j01018 fundamental research funds for the central university 2013121001

classification of category j modules for divergence zero vector fields on a torus abstract we consider a category of modules that admit compatible actions of the commutative algebra of laurent polynomials and the lie algebra of divergence zero vector fields on a torus and have a weight decomposition with finite dimensional weight spaces we classify indecomposable and irreducible modules in this category

central extensions of current groups in two dimensions the paper is devoted to generalization of the theory of loop groups to the two dimensional case to every complex riemann surface we assign a central extension of the group of smooth maps from this surface to a simple complex lie group g by the jacobian of this surface this extension is topologically nontrivial as in the loop group case orbits of coadjoint representation of this extension correspond to equivalence classes of holomorphic principalg bundles over the surface when the surface is the torus elliptic curve classification of coadjoint orbits is related to linear difference equations in one variable and to classification of conjugacy classes in the loop group we study integral orbits for which the kirillov kostant form is a curvature form for some principal torus bundle the number of such orbits for a given level is finite as in the loop group case conjecturedly they correspond to analogues of integrable modules occurring in conformal field theory

partial classification of modules for lie algebra of diffeomorphisms of d dimensional torus we consider the lie algebra of the group of diffeomorphisms of a d dimensional torus which is also known to be the algebra of derivations on a laurent polynomial ring a in d commuting variables denoted by der a the universal central extension of der a for d 1 is the so called virasoro algebra the connection between virasoro algebra and physics is well known see for example the book on conformal field theory by di francesco mathieu and senechal in this paper we classify a der a modules which are irreducible and have finite dimensional weight spaces earlier larsson constructed a large class of modules the so called tensor fields based on gld modules which are also a modules we prove that they exhaust all a der a irreducible modules

a characterization of affine kac moody lie algebras we give a new characterization of the affine kac moody algebras in terms of extended affine lie algebras we also present new realizations of the twisted affine kac moody algebras

generalized scale invariance in the atmosphere and fractal models of rain in recent years there has been considerable interest in stochastic rain models by developing new ideas about scale invariance and intermittency we argue that the scope of such models can be greatly extended the notions of scale invariance intermittency and the associated idea of fractal dimension have lately gained considerable ground particularly in the context of extremely variable phenomena such as those found in the mesoscale and in hydrodynamic turbulence we review some relevant work and argue that the atmosphere respects a symmetry principle that we call generalized scale invariance in which the statistical properties of the small and large scale are related to each other by a magnification coupled with a differential stratification due to gravity and differential rotation due to the coriolis force we further argue that the extremely erratic intermittent nature of the atmosphere is characterized by scale invariant fractal measures leading to hyperbolic fat tailed probability distributions of the fluctuations the standard statistical methods based on exponential fall offs in both correlations and probability distributions are inappropriate when the variability is of this type we show how both the scaling and intermittency may be exploited to develop extremely variable stochastic models of rain although the models examined here are the simplest of a family of extremely variable processes depending on only two radar determined parameters they lead to realizations possessing many realistic features of the rainfield including complexity of form clustering and bands at all scales as well as differential stratification and rotation finally we point to weaknesses in the models in particular their monodimensional nature and suggest possible improvements

irreducible finite dimensional representations of equivariant map algebras suppose a finite group acts on a scheme x and a finite dimensional lie algebra g the corresponding equivariant map algebra is the lie algebra m of equivariant regular maps from x to g we classify the irreducible finite dimensional representations of these algebras in particu lar we show that all such representations are tensor products of evaluation representations and one dimensional representations and we establish conditions ensuring that they are all evaluation representations for example this is always the case if m is perfect our results can be applied to multiloop algebras current algebras the onsager algebra and the tetrahedron algebra doing so we easily recover the known classifications of irreducible finite dimensional representations of these algebras moreover we obtain previously unknown classifica tions of irreducible finite dimensional representations of other types of equivariant map algebras such as the generalized onsager algebra

irreducible representations for toroidal lie algebras abstract in this work a large number of irreducible representations with finite dimensional weight spaces are constructed for some toroidal lie algebras to accomplish this we develop a general theory of z n graded lie algebras with polynomial multiplication we construct modules by the standard inducing procedure and study their irreducible quotients using the vertex operator technics

affine lie algebras and product sum identities abstract we provide four different decompositions for a special infinite product first studied by i schur our product sum decomposition gives two more correspondences between subsets of partitions with parts congruent to 1 or 5 modulo 6 our method uses a special vertex representation of affine lie algebra c 3 1 and admissible representations of a 1 1 as well as quintuple product identity

hermitian representations of the extended affine lie algebra gl2 cq abstract we use the idea of free fields to obtain highest weight representations for the extended affine lie algebra gl 2 c q coordinatized by the quantum torus c q and go on to construct a contravariant hermitian form we further give a necessary and sufficient condition such that the contravariant hermitian form is positive definite

twisted γ lie algebras and their vertex operator representations let be a generic subgroup of the multiplicative group c of nonzero complex numbers we define a class of lie algebras associated to called twisted lie algebras which are natural generalizations of the twisted affine lie algebras starting from an arbitrary even sublattice q of zn and an arbitrary finite order isometry of zn preserving q we construct a family of twisted vertex operators acting on generalized fock spaces which afford irreducible representations for certain twisted lie algebras as an application this recovers a number of known vertex operator realizations for infinite dimensional lie algebras such as twisted affine lie algebras extended affine lie algebras of type a trigonometric lie algebras of series a and b unitary lie algebras and bc graded lie algebras

borel subalgebras and categories of highest weight modules for toroidal lie algebras abstract in this article we begin an investigation of the conjugacy classes of borel subalgebras together with verma modules induced from standard borel subalgebras of a toroidal lie algebra t in two variables we define for each highest weight a category o of representations of t that contain these verma modules and show that when a certain central element acts nontrivially this category is equivalent to the category o m for an extension of a suitable affine kac moody algebra m t from this equivalence we obtain a bgg type resolution and bgg duality theorem in the setting of o

vertex representations for the ν 1 toroidal lie algebra of type bl abstract we give vertex operator constructions for the toroidal lie algebra of type b l 1 l 2 we prove that the subquotients of the modules are completely reducible and give the irreducible decomposition

a spectral theory of rainfall intensity at the meso β scale the available empirical descriptions of extratropical cyclonic storms are employed to formulate a physically realistic stochastic representation of the ground level rainfall intensity field in space and time the stochastic representation is based on three component stochastic point processes which possess the general features of the embedding of rain cells within small mesoscale areas within large mesoscale areas within synoptic storms certain scale idealizations and assumptions on functional forms which qualitatively reflect the physical features lead to a closed form expression for the covariance function i e the real space time spectrum of the rainfall intensity field the theoretical spectrum explains the empirical spectral features observed by zawadzki almost a decade ago of particular interest and importance in this connection is an explanation of the empirical observation that the taylorian propogation of the fine scale structure via a transformation of time to space through the storm velocity holds only for a small time lag and not throughout the results here indicate the extent of this lag in terms of the characteristic scales associated with cell durations cellular birthrates and velocities etc

vertex operators for non simply laced algebras a vertex operator construction is given for the level one representations of the affine kac moody algebras associated with non simply laced finite dimensional lie algebras using free boson and interacting fermion fields the fermion fields are constructed explicitly and a detailed discussion is given of the theory of the cocycles necessary for this and other vertex operator constructions the construction is related in detail to the folding of dynkin diagrams and a generalisation of it yields freudenthal s magic square

on self similar lie algebras and virtual endomorphisms we introduce the notion of virtual endomorphisms of lie algebras and use it as an approach for constructing self similarity of lie algebras this is done in particular for a class of metabelian lie algebras having homological type fp n which are lie algebra analogues of lamplighter groups we establish several criteria when the existence of virtual endomorphism implies a self similar lie structure furthermore we prove that the classical lie algebra sl n k where char k does not divide n affords non trivial faithful self similarity

the alternative torus and the structure of elliptic quasi simple lie algebras of type we present the complete classification of the tame irreducible elliptic quasi simple lie algebras of type a2 and in particular specialize on the case where the coordinates are not associative here the coordinates are cayley dickson algebras over laurent polynomial rings in v 3 variables which we call alternative tori in giving our classification we need to present much information on these alternative tori and the lie algebras coordinatized by them

the irreducible modules for the derivations of the rational quantum torus abstract let c q be the quantum torus associated with the d d matrix q q i j where q i j are roots of unity with q i i 1 and q i j 1 q j i for all 1 i j d let der c q be the lie algebra of all the derivations of c q in this paper we define the lie algebra der c q c q and classify its irreducible modules with finite dimensional weight spaces these modules under certain conditions turn out to be of the form v c q where v is a finite dimensional irreducible g l d module

central extensions of current groups in this paper we study central extensions of the identity component g of the lie group c m k of smooth maps from a compact manifold m into a lie group k which might be infinite dimensional we restrict our attention to lie algebra cocycles of the form d where y is a symmetric invariant bilinear map on the lie algebra of k and the values of lie in 1 m y dc m y for such cocycles we show that a corresponding central lie group extension exists if and only if this is the case for m 1 if k is finite dimensional semisimple this implies the existence of a universal central lie group extension of g the groups diff m and c m k act naturally on g by automorphisms we also show that these smooth actions can be lifted to smooth actions on the central extension if it also is a central extension of the universal covering group g of g

magnetic hydrodynamics with asymmetric stress tensor in this paper we study equations of magnetic hydrodynamics with a stress tensor we interpret this system as the generalized euler equation associated with an abelian extension of the lie algebra of vector fields with a nontrivial 2 cocycle we use the lie algebra approach to prove the energy conservation law and the conservation of cross helicity

a note on tailbiting codes and their feedback encoders tailbiting codes encoded by feedback convolutional encoders are studied a condition for when tailbiting will work is given and it is described how the encoder starting state can be obtained for feedback encoders in both controller and observer canonical forms finally results from a search for systematic feedback encoders that encode tailbiting codes with good decoding bit error probabilities are presented

quantum tori and the structure of elliptic quasi simple lie algebras abstract we study and classify those tame irreducible elliptic quasi simple lie algebras which are simply laced and of rankl 3 the first step is to identify the core of such an algebra up to central isogeny by identifying the coordinates when the type isdorethe coordinates are laurent polynomials in variables while for typeathe coordinates can be any quantum torus in variables the next step is to study the universal central extension as well as the derivation algebra of the core these are related to the first connes cyclic homology group of the coordinates the final step is to use this information to give constructions of lie algebras which we then prove yield representatives of all isomorphism classes of the above types of algebras

elliptic lie algebras and tubular algebras abstract this article is to study relations between tubular algebras of ringel and elliptic lie algebras in the sense of saito yoshii using the explicit structure of the derived categories of tubular algebras given by happel ringel we prove that the elliptic lie algebra of type d 4 1 1 e 6 1 1 e 7 1 1 or e 8 1 1 is isomorphic to the ringel hall lie algebra of the root category of the tubular algebra with the same type as a by product of our proof we obtain a chevalley basis of the elliptic lie algebra following indecomposable objects of the root category of the corresponding tubular algebra this can be viewed as an analogue of the frenkel malkin vybornov theorem in which they described a chevalley basis for each untwisted affine kac moody lie algebra by using indecomposable representations of the corresponding affine quiver

an extension of the korteweg de vries hierarchy arising from a representation of a toroidal lie algebra abstract in this article we show how to construct hierarchies of partial differential equations from the vertex operator representations of toroidal lie algebras in the smallest example rank 2 toroidal cover of sl2 we obtain an extension of the kdv hierarchy we use the action of the corresponding infinite dimensional group to construct solutions for these non linear pdes

integrable modules for twisted toroidal extended affine lie algebras abstract in this paper we classify the irreducible integrable modules for the twisted toroidal extended affine lie algebras twisted toroidal eala in short with finite dimensional weight spaces when the finite dimensional center acts non trivially using an automorphism we reduce to the case where k 0 acts non trivially and k i 1 i n act trivially twisted toroidal eala has a natural triangular decomposition and we prove that any irreducible integrable module of it with finite dimensional weight spaces is a highest weight module with respect to the above triangular decomposition the highest weight space is an irreducible module for the zeroth component of the twisted toroidal eala we then describe the highest weight space in detail

algebras of diffeomorphisms of the n torus the general algebra d n v of infinitesimal diffeomorphisms of the n torus s1 n involving generators lv m depending on a structure vector v cn and a vector valued index m zn is constructed several results are proved for this algebra special cases of the algebra were previously presented in ramos shrock e ramos and r e shrock int j mod phys a 4 4279 1989 the concept of the q rank of the space v of structure vectors denoted rq v is defined and certain related cartan matrices are introduced it is shown that d n v as an ungraded algebra is simple if and only if rq v n i e the q rank of v is maximal a classification under isomorphisms is given for the algebra and is shown to reduce to a classification of the cartan matrices the space of structure vectors is isomorphic to the unique cartan subalgebra a number of properties concerning the central extensions of these algebras are then proved for the case dim v 1 rq v n it is shown that the central extension is unique fo

equivariant map superalgebras suppose a group gamma acts on a scheme x and a lie superalgebra mathfrak g the corresponding equivariant map superalgebra is the lie superalgebra of equivariant regular maps from x to mathfrak g we classify the irreducible finite dimensional modules for these superalgebras under the assumptions that the coordinate ring of x is finitely generated gamma is finite abelian and acts freely on the rational points of x and mathfrak g is a basic classical lie superalgebra or mathfrak sl n n n ge 1 if gamma is trivial we show that they are all tensor products of generalized evaluation modules and are parameterized by a certain set of equivariant finitely supported maps defined on x furthermore in the case that the even part of mathfrak g is semisimple we show that all such modules are in fact tensor products of evaluation modules on the other hand if the even part of mathfrak g is not semisimple more generally if mathfrak g is of type i we introduce a natural generalization of kac modules and show that all irreducible finite dimensional modules are quotients of these as a special case our results give the first classification of the irreducible finite dimensional modules for twisted loop superalgebras

vertex operators arising from the homogeneous realization for we use the underlying fock space for the homogeneous vertex operator representation of the affine lie algebra to construct a family of vertex operators as an application an irreducible module for an extended affine lie algebra of type a n 1 coordinatized by a quantum torus q of 2 variables or 3 variables is obtained moreover this module turns out to be a highest weight module which is an analog of the basic module for affine lie algebras

bosonic realization of toroidal lie algebras of classical types we use fermionic operators to construct toroidal lie algebras of classical types including in particular symplectic affine algebras which are first realized by fermions

highest weight modules over pre exp polynomial lie algebras abstract in this paper we introduce pre exp polynomial lie algebras which include loop algebras virasoro like algebras and some quantum torus lie algebras we study highest weight representations of these z n 1 graded lie algebras more precisely we show that non graded and graded irreducible highest weight modules with the same highest weight simultaneously have all finite dimensional weight spaces or not and they have all finite dimensional weight spaces if and only if the highest weight is an exp polynomial highest weight we also show that non graded and graded highest weight verma modules with the same highest weight are simultaneously irreducible or not and we determine necessary and sufficient conditions for a verma module to be irreducible

structure and representation for a class of infinite dimensional lie algebras abstract let a be a commutative associative algebra over the complex field c and g be the complexification of the real lie algebra so 3 for any fixed elements e 1 e 2 e 3 a we define a lie algebra l e 1 e 2 e 3 g a with lie bracket given by 1 2 when the associative algebra a is the laurent polynomial algebra c t 1 1 t 1 we determine its derivation lie algebra der l and universal central extension l we also give a vertex operator representation for the lie algebra l this new class of lie algebras includes the affine lie algebra a 1 1 and the toroidal lie algebras of type a 1 we note that in general this kind of lie algebras is not z graded

on the polynomial representations of current algebras abstract we obtain a sufficient condition for a representation of a lie algebra of the form l g where g is a finite dimensional simple lie algebra over an algebraically closed field f of zero characteristic and is an associative commutative algebra over f to be polynomial as a corollary we classify integrable graded irreducible modules over an extended loop algebra with finite dimensional homogeneous spaces the criteria is applied also to irreducible conformal modules over current algebras

wn and wn module structures on u hn abstract let h n be the cartan subalgebra of the witt algebras w n der c t 1 t 2 t n and w n der c t 1 1 t 2 1 t n 1 where 1 n in this paper we classify the modules over w n and over w n which are free u h n modules of rank 1 these are the w n modules n a s for some n 1 n c n a c and s 1 2 n and w n modules n a for some n c n and some a c

vertex operators of g2 1 and bl 1 the vertex operator construction is given for the level one representations of the affine kac moody algebras g2 1 and bl 1

an optimal circular viterbi decoder for the bounded distance criterion we propose a viterbi type decoder for tailbiting trellis codes that works by traversing the tailbiting circle somewhat more than once the traversal is the least possible for any bounded distance viterbi decoder procedures are given that compute this minimum unlike previous decoders of the type the new scheme does not suffer limit cycles or from pseudocodewords the bit error rate is compared to that of bahl cocke jelinek raviv and maximum likelihood decoding

irreducible representations of virasoro toroidal lie algebras toroidal lie algebras and their vertex operator representations were introduced in mey and a class of indecomposable modules were investigated in this work we extend the toroidal algebra by the virasoro algebra thus constructing a semi direct product algebra containing the toroidal algebra as an ideal and the virasoro algebra as a subalgebra with the use of vertex operators and certain oscillator representations of the virasoro algebra it is proved that the corresponding fock space gives rise to a class of irreducible modules for the virasoro toroidal algebra

best short rate 1 2 tailbiting codes for the bit error rate criterion we give a method of finding convolutional codes with minimum bit error rate ber that combines ideas of importance sampling monte carlo integration and maximum a posteriori probability decoding the method is applied to rate 1 2 tailbiting convolutional coding both feedforward and feedback systematic tables of ber minimizing encoders are given for memories 2 5 and tailbiting size 5 40 over a range of good and bad binary symmetric and additive white gaussian noise channels the best generators for these cases are in general all different and are not necessarily the generators that optimize distance the best generators for bad channels are always systematic the best when the channel quality is known are usually feedforward but when it is unknown they are feedback systematic the best generators in good channels are predicted by a union bound technique

simple toroidal vertex algebras and their irreducible modules abstract in this paper we continue the study on toroidal vertex algebras initiated in 15 to study concrete toroidal vertex algebras associated to toroidal lie algebra l r g g l r where g is an untwisted affine lie algebra and l r c t 1 1 t r 1 we first construct an r 1 toroidal vertex algebra v t 0 and show that the category of restricted l r g modules is canonically isomorphic to that of v t 0 modules let c denote the standard central element of g and set s c u l r c c we furthermore study a distinguished subalgebra of v t 0 denoted by v s c 0 we show that graded simple quotient toroidal vertex algebras of v s c 0 are parametrized by a z r graded ring homomorphism s c l r such that im is a z r graded simple s c module denote by l 0 the simple quotient r 1 toroidal vertex algebra of v s c 0 associated to we determine for which l 0 is an integrable l r g module and we then classify irreducible l 0 modules for such a for our need we also obtain various general results

extended diffeomorphism algebras and trajectories in jet space let the dro diffeomorphism reparametrization observer algebra dro n be the extension of diff n diff 1 by its four inequivalent virasoro like cocycles here diff n is the diffeomorphism algebra in n dimensional spacetime and diff 1 describes reparametrizations of trajectories in the space of tensor valued p jets dro n has a fock module for each p and each representation of gl n analogous representations for gauge algebras higher dimensional kac moody algebras are also given the reparametrization symmetry can be eliminated by a gauge fixing procedure resulting in previously discovered modules in this process two dro n cocycles transmute into anisotropic cocycles for diff n thus the fock modules of toroidal lie algebras and their derivation algebras are geometrically explained

vertex representations for n toroidal lie algebras and a generalization of the virasoro algebra vertex representations are obtained for toroidal lie algebras for any number of variables these representations afford representations of certainn variable generalizations of the virasoro algebra that are abelian extensions of the lie algebra of vector fields on a torus

irreducible representations of the lie algebra of the diffeomorphisms of ad dimensional torus in this paper we investigate the irreducibility of certain modules for the lie algebra of diffeomorphisms of torus t the lie algebra of diffeomorw 1 1 x phisms can be described as the derivations of a s c t t see 1 d w x w x rss we denote this lie algebra by der a larsson l1 constructed a functor from gl modules to der a modules in this paper we prove that d the image of a finite dimensional irreducible gl module is most often d irreducible the only exceptions are fundamental modules and the onedimensional modules in these cases we describe the sub modules and the quotients surprisingly the same class of modules image of finite dimen w x sional gl module are also constructed in e without any reference to d gl modules they are motivated by the vertex operator constructions in d w x em more details near the end of this introduction we will now describe our results in more detail let gl be the d lie algebras of d d matrices over complex numbers c let gl s sl d d c id where sl is the finite dimensional simple lie algebra of trace zero d matrices and id the identity matrix which is central it is well known that finite dimensional irreducible modules and dominant integral weights are in one one correspondence for a finite dimensional simple lie algebra so let v c be finite dimensional irreducible sl module corresponding to a d dominant integral weight c let id the central element act by a complex number b and denote the corresponding gl module by v c b d a d d larsson defined see 1 6 a functor f for a belonging to c rz from w x gl modules to der a modules in l1 these modules are weight modules d

vertex representations of quantum affine algebras we construct vertex representations of quantum affine algebras of ade type which were first introduced in greater generality by drinfeld and jimbo the limiting special case of our construction is the untwisted vertex representation of affine lie algebras of frenkel kac and segal our representation is given by means of a new type of vertex operator corresponding to the simple roots and satisfying the defining relations in the case of the quantum affine algebra of type a we introduce vertex operators corresponding to all the roots and determine their commutation relations this provides an analogue of a chevalley basis of the affine lie algebra unk n in the basic representation

lie algebras graded by finite root systems and the intersection matrix algebras of slodowy this paper is about toroidal lie algebras certain intersection matrix lie algebras defined by slodowy and their relationship to one another and to certain lie algebra analogues of steinberg groups the main result of the paper is the identification of the intersection matrix algebras arising from multiply affinized cartan matrices of types a d and e with certain steinberg lie algebras and toroidal lie algebras propositions 5 9 and 5 10 a major part of the paper studies and classifies lie algebras graded by finite root systems these become the princi pal tool in our analysis of intersection matrix algebras each lie algebra graded by a simply laced finite root system of rank 2 has attached to it an algebra which according to the type and rank is either commutative and associative only associative or alternative all these possibilities occur in our description of inter section matrix algebras let r be any associative algebra with identity not necessarily finite dimen sional over a field k of characteristic 0 for each positive integer n the associative algebra m r of n n matrices with coefficients in r forms a lie algebra over k under the commutator product we denote this lie algebra by ol r let eis be the i j matrix unit of m r and assume that n 2 the subalgebra e r of oi r generated by the elements reis r r i 4 j is an ideal of 91 r and is perfect i e it is its own derived algebra now any perfect lie algebra o has a universal central extension also perfect called a universal covering algebra u c a of o ga so in particular e r has a u c a that we will denote by t r we define 112 r by the exact sequence 0 1 0 f2 r t r e r 0 dedicated to our teacher maria j wonenburger both authors gratefully acknowledge the support of the natural sciences and engineering research council of canada

integrable representations for the twisted full toroidal lie algebras the purpose of this work is to classify irreducible integrable modules of the twisted full toroidal lie algebra with finite dimensional weight spaces and non zero central charges there are three families of such modules two of which are classified

twisted vertex representations of quantum affine algebras recent interests in quantum groups are stimulated by their marvelous relations with quantum yang baxter equations conformal field theory invariants of links and knots and q hypergeometric series besides understanding the reason of the appearance of quantum groups in both mathematics and theoretical physics there is a natural problem of finding q deformations or quantum analogues of known structures quantum groups were first defined by drinfeld 2 and jimbo 9 also see 4 as a q deformation of the universal enveloping algebras of the kacmoody algebras in the work of trigonometric solutions of yang baxter equations in the same spirit it was shown in 13 14 that there exists a 1 1 correspondence between the integrable highest weight representations of symmetrizable kac moody algebras and those of the corresponding quantum groups where both spaces have the same dimension in the case of generic q i e q is not a root of unity moreover one can be very explicit in the case of quantum gl n to write down the irreducible highest weight representations quantum affine algebras are the quantum groups associated to affine lie algebras following drinfeld s realization 3 of q analog of loop algebras the vertex representation of untwisted simply laced quantum affine algebras was constructed in frenkel jing 6 which is a q deformation of frenkel kac 7 and segal 15 construction in the theory of affine lie algebras subsequently the same was done for the quantum affine algebra of type b in 1 in the present work we construct vertex representations of quantum affine algebras twisted by an automorphism of the dynkin diagram which generalizes certain important cases in the ordinary twisted vertex operator calculus 5

representations of twisted multi loop lie algebras abstract this paper describes finite dimensional irreducible representations of twisted multi loop lie algebras these representations are given in terms of the representations of finite dimensional semisimple lie algebras