symplectic lie algebras with degenerate center abstract every symplectic lie algebra with degenerate including non abelian nilpotent symplectic lie algebras has the structure of a quadratic extension we give a standard model and describe the equivalence classes on the level of corresponding quadratic cohomology sets finally we give a scheme to classify the isomorphism classes of symplectic lie algebras with degenerate center we also give a classification scheme for nilpotent symplectic lie algebras and compute a complete list of all 6 dimensional nilpotent symplectic lie algebras which removes inaccuracies in an older list

realizations of conformal current type lie algebras in this paper we obtain the realizations of some infinite dimensional lie algebras named conformal current type lie algebras in terms of a two dimensional novikov algebra and its deformations furthermore ovsienko and roger s loop cotangent virasoro algebra which can be regarded as a nice generalization of the virasoro algebra with two space variables is naturally realized as an affinization of the tensor product of a deformation of the two dimensional novikov algebra and the laurent polynomial algebra these realizations shed new light on various aspects of the structure and representation theory of the corresponding infinite dimensional lie algebras

the atiyah bott patodi method in deformation quantization we give a new proof of the index theorem for deformation quantization following the atiyah bott patodi scheme the main ingredient consists of tamarkin s theorem on topological invariants of symplectic connections which is a symplectic analog of the well known theorems for riemannian connections

deformation quantizations with separation of variables on a kahler manifold we give a simple geometric description of all formal differentiable deformation quantizations on a kahler manifoldm such that for each open subsetu m multiplication from the left by a holomorphic function and from the right by an antiholomorphic function onu coincides with the pointwise multiplication by these functions we show that these quantizations are in 1 1 correspondence with the formal deformations of the original kahler metrics onm

an mx g 1 unreliable retrial queue with two phases of service and bernoulli admission mechanism this paper deals with the steady state behaviour of an m x g 1 retrial queue with an additional second phase of optional service and unreliable server where breakdowns occur randomly at any instant while serving the customers further concept of bernoulli admission mechanism is also introduced in the model this model generalizes both the classical m x g 1 retrial queue subject to random breakdown and bernoulli admission mechanism as well as m x g 1 queue with second optional service and unreliable server we carry out an extensive analysis of this model

on an infinite dimensional lie algebra of virasoro type in this paper we study an infinite dimensional lie algebra of virasoro type which is realized as an affinization of a two dimensional novikov algebra it is a special deformation of the lie algebra of differential operators on a circle of order at most 1 there is an explicit construction of a vertex algebra associated with the lie algebra we determine all derivations of this lie algebra in terms of some derivations and centroids of the corresponding novikov algebra the universal central extension of this lie algebra is also determined

hermitian einstein metrics from noncommutative u 1 instantons we show that hermitian einstein metrics can be locally constructed by a map from anti self dual two forms on euclidean r4 to symmetric two tensors introduced in yang and salizzoni phys rev lett 96 201602 2006 e print arxiv hep th 0512215 this correspondence is valid not only for a commutative space but also for a noncommutative space we choose u 1 instantons on a noncommutative c2 as the self dual two form from which we derive a family of hermitian einstein metrics we also discuss the condition when the metric becomes kahler we show that hermitian einstein metrics can be locally constructed by a map from anti self dual two forms on euclidean r4 to symmetric two tensors introduced in yang and salizzoni phys rev lett 96 201602 2006 e print arxiv hep th 0512215 this correspondence is valid not only for a commutative space but also for a noncommutative space we choose u 1 instantons on a noncommutative c2 as the self dual two form from which we derive a family of hermitian einstein metrics we also discuss the condition when the metric becomes kahler

flat affine or projective geometries on lie groups abstract this paper deals essentially with affine or projective transformations of lie groups endowed with a flat left invariant affine or projective structure these groups are called flat affine or flat projective lie groups we give necessary and sufficient conditions for the existence of flat left invariant projective structures on lie groups we also determine lie groups admitting flat bi invariant affine or projective structures these groups could play an essential role in the study of homogeneous spaces m g h having a flat affine or flat projective structures invariant under the natural action of g on m a medina asked several years ago if the group of affine transformations of a flat affine lie group is a flat projective lie group in this work we provide a partial positive answer to this question

the classification of novikov algebras in low dimensions novikov algebras were introduced in connection with the poisson brackets of hydrodynamic type and hamiltonian operators in the formal variational calculus for further our understanding and physical applications we give a classification of novikov algebras in dimensions two and three in this paper

a formal model of berezin toeplitz quantization we give a new construction of symbols of the differential operators on the sections of a quantum line bundle l over a kahler manifold m using the natural contravariant connection on l these symbols are the functions on the tangent bundle tm polynomial on fibres for high tensor powers of l the asymptotics of the composition of these symbols leads to the star product of a deformation quantization with separation of variables on tm corresponding to some pseudo kahler structure on tm surprisingly this star product is intimately related to the formal symplectic groupoid with separation of variables over m we extend the star product on tm to generalized functions supported on the zero section of tm the resulting algebra of generalized functions contains an idempotent element which can be thought of as a natural counterpart of the bergman projection operator using this idempotent we define an algebra of toeplitz elements and show that it is naturally isomorphic to the algebra of berezin toeplitz deformation quantization on m

on the central extensions of poisson brackets of hydrodynamic type poisson brackets of hydrodynamic type were introduced to construct a theory of conservation system of hydrodynamic type they lead to the algebraic and differentially geometrical theory of local translationally invariant lie algebras of first order frobenius type algebras and novikov algebras one of the main ways to construct new examples of these algebras and their corresponding poisson brackets is through the central extensions in balinskii a a and novikov s p 1985 sov math dokl 32 228 31 there is a general theory of the central extensions in this paper we give a further detailed study of two non trivial types of novikov algebras which directly decide an important kind of central extension of the poisson brackets we find that the novikov algebras in the case 3 are in the case 0 and these two cases coincide in dimension 3 moreover they also coincide for the transitive cases in dimension 4

pseudo kahler quantization on flag manifolds a unified approach to geometric symbol and deformation quantizations on a generalized flag manifold endowed with an invariant pseudo kahler structure is proposed in particular cases we arrive at berezin s quantization via covariant and contravariant symbols

novikov poisson algebras abstract we classify novikov poisson algebras whose novikov algebras are simple with an idempotent element moreover a class of simple novikov algebras without idempotent elements is constructed through novikov poisson algebras certain new simple lie superalgebras induced by novikov poisson algebras are introduced

classification of balinsky novikov superalgebras with dimension 2 2 the notion of balinsky novikov bn superalgebra was introduced to construct super virasoro type lie superalgebras we classify the 2 2 dimensional complex bn superalgebras whose odd parts products are not zero in addition to the known results on the classification of 2 2 dimensional novikov superalgebras we give an explicit comparison among them and their associated lie superalgebras as an application we construct some lie superalgebras whose even parts are the w 2 2 lie algebra finally we reformulate the classification results in terms of the even parts being the known classification results of two dimensional novikov algebras

on fermionic novikov algebras novikov algebras were introduced in connection with the poisson brackets of hydrodynamic type and hamiltonian operators in formal variational calculus they are a class of left symmetric algebras with commutative right multiplication operators which can be viewed as bosonic fermionic novikov algebras are a class of left symmetric algebras with anti commutative right multiplication operators they correspond to a certain hamiltonian superoperator in a supervariable in this paper we commence a study on fermionic novikov algebras from the algebraic point of view we will show that any fermionic novikov algebra in dimension 3 must be bosonic moreover we give the classification of real fermionic novikov algebras on four dimensional nilpotent lie algebras and some examples in higher dimensions as a corollary we obtain kinds of four dimensional real fermionic novikov algebras which are not bosonic all of these examples will serve as a guide for further development including the application in physics

expansion formulas for terminating balanced 4 f 3 series from the biedenharn elliot identity for su 1 1 in a recent paper george gasper contemp math 254 2000 187 proved some expansion formulas for terminating balanced hypergeometric series of type 4f3 with unit argument in this article we show how one easily derives such expansion formulas from the biedenharn elliot identity for the lie algebra su 1 1 furthermore we give a rather systematic method for determining when two apparently different expansion formulas are the same up to transformation formulas this is a rather nice application of the so called invariance groups of hypergeometric series the method extends to other cases we briefly indicate how it works in the case of expansion formulas for 3f2 series we conclude with some basic analogues and show their relation with the askey wilson polynomials

on gammelgaard s formula for a star product with separation of variables we show that gammelgaard s formula expressing a star product with separation of variables on a pseudo kahler manifold in terms of directed graphs without cycles is equivalent to an inversion formula for an operator on a formal fock space we prove this inversion formula directly and thus offer an alternative approach to gammelgaard s formula which gives more insight into the question why the directed graphs in his formula have no cycles

invariance groups of transformations of basic hypergeometric series we show that certain two term transformation formulas between basic hypergeometric series can easily be described by means of invariance groups for the transformations of nonterminating 3 2 series and those of terminating balanced 4 3 series these invariance groups are symmetric groups for transformations of 2 1 series the invariance group is the dihedral group of order 12 transformations of terminating 3 2 series are described by means of some subgroup of s6 and finally the invariance group of transformations of very well poised nonterminating 8 7 series is shown to be isomorphic to the weyl group of a root system of type d5

poisson arrivals see time averages in many stochastic models particularly in queueing theory poisson arrivals both observe see a stochastic process and interact with it in particular cases and or under restrictive assumptions it has been shown that the fraction of arrivals that see the process in some state is equal to the fraction of time the process is in that state in this paper we present a proof of this result under one basic assumption the process being observed cannot anticipate the future jumps of the poisson process

double extension symplectique d un groupe de lie symplectique resume lie groups carrying a left invariant symplectic form symplectic groups are described in terms of semi direct product of lie groups or symplectic reduction and principal fiber bundles with affine fiber we give a generalization of medina and revoy s symplectic double extension which realizes a symplectic group as the reduction of another symplectic group we show that every group obtained by this process carries an invariant lagrangian foliation such that the affine structure defined by the simplectic form over each leaf is complete

symplectic structures on quadratic lie algebras abstract we study quadratic lie algebras over a field k of null characteristic which admit at the same time a symplectic structure we see that if k is algebraically closed every such lie algebra may be constructed as the t extension of a nilpotent lie algebra admitting an invertible derivation and also as the double extension of another quadratic symplectic lie algebra by the one dimensional lie algebra finally we prove that every symplectic quadratic lie algebra is a special symplectic manin algebra and we give an inductive description in terms of symplectic quadratic double extensions

coxeter group actions on saalschutzian f34 1 series and very well poised f67 1 series abstract in this paper we consider a function l x l a b c d e f g which can be written as a linear combination of two saalschutzian f 3 4 1 hypergeometric series or as a very well poised f 6 7 1 hypergeometric series we explore two term and three term relations satisfied by the l function and put them in the framework of group theory we prove a fundamental two term relation satisfied by the l function and show that this relation implies that the coxeter group w d 5 which has 1920 elements is an invariance group for l x the invariance relations for l x are given two classifications based on two double coset decompositions of the invariance group the fundamental two term relation is shown to generalize classical results about hypergeometric series we derive thomae s identity for f 2 3 1 series bailey s identity for terminating saalschutzian f 3 4 1 series and barnes second lemma as consequences we further explore three term relations satisfied by l a b c d e f g the group that governs the three term relations is shown to be isomorphic to the coxeter group w d 6 which has 23 040 elements based on the right cosets of w d 5 in w d 6 we demonstrate the existence of 220 three term relations satisfied by the l function that fall into two families according to the notion of l coherence the complexity of the coefficients in front of the l functions in the three term relations is studied and is shown to also depend on l coherence

the realization of non transitive novikov algebras novikov algebras were introduced in connection with hydrodynamic type poisson brackets and hamiltonian operators in the formal variational calculus we have given a kind of realization of transitive novikov algebras through the novikov algebras given by s gelfand and their compatible infinitesimal deformations in bai and meng 2001 j phys a math gen 34 3363 72 as a further and continuous study we extend this realization theory to the non transitive novikov algebras in the paper in two and three dimensions we find that all non transitive novikov algebras also can be realized as the novikov algebras given by s gelfand and their compatible infinitesimal deformations moreover they have simpler formulae

gauge theories in noncommutative homogeneous kahler manifolds we construct a gauge theory on a noncommutative homogeneous kahler manifold where we employ the deformation quantization with separation of variables for kahler manifolds formulated by karabegov a key point in this construction is to obtaining vector fields which act as inner derivations for the deformation quantization we give an explicit construction of this gauge theory on noncommutative cpn and noncommutative chn

deformation quantization of almost kahler models and lagrange finsler spaces finsler and lagrange spaces can be equivalently represented as almost kahler manifolds endowed with a metric compatible canonical distinguished connection structure generalizing the levi civita connection the goal of this paper is to perform a natural fedosov type deformation quantization of such geometries all constructions are canonically derived for regular lagrangians and or fundamental finsler functions on tangent bundles

berezin s quantization on flag manifolds and spherical modules we show that the theory of spherical harish chandra modules naturally gives rise to berezin s symbol quantization on generalized flag manifolds it provides constructions of symbol algebras and of their representations for covariant and contravariant symbols and also for symbols which so far have no explicit definition for all these symbol algebras we give a general proof of the correspondence principle introduction berezin s quantization on a symplectic manifold q see 1 is givexl by a family of associative algebras h whose elements are smooth functions on q together with their representations in hilbert spaces hh where the parameter h plays the role of the planck constant the rnultiplication h in ah must satisfy the so called correspondence principle as h o a formal definition is given in section 1 representation of the algebra ah in hh maps a function h c ah to the operator a in hh in that case the function h is called a symbol of the operator f the concrete examples of quantizatiorls are usually based on explicit collstructions of symbols see 1 2 in this paper we show how the theory of spherical harish chazdra modules naturally provides the algebras of covariant arld corltravariant syrrlbols on generalized flag manifolds moreover it also gives rise to the algebras of symbols which so far have no general construction or definition as in the case of covariant and contravariant symbols for all these symbol algebras we give a general proof of the correspondence principle we also prove the conjecture from 3 on rational dependence of the product c h g on h on an arbitrary generalized flag manifold 1 teie definition of qijantization we will give now a formal definition of quantization on a syrrlplectic manifold q let f be a set of positive numbers with a limit point 0 for each h c f let ah be an algebra which is a linear subspace of c q with a multiplication h and a given representation in a hilbert space hh define a uh ah and let a be dense in c q e these data d termine a quantization on q if for f g c and h o the correspondence principle holds l s h g fg h f h g g h f tf 9 qreceived by the editors december 14 1994 and in revised form june 14 1996 199l mathematics subject classification primary 58f06 secondary 22e47

poincare cartan class and deformation quantization of kahler manifolds we introduce a complete invariant for weyl manifolds called a poincare cartan class applying the constructions of the weyl manifold to complex manifolds via the poincare cartan class we propose the notion of a noncommutative kahler manifold for a given kahler manifold the necessary and sufficient condition for a weyl manifold to be a noncommutative kahler manifold is given in particular there exists a noncommutative kahler manifold for any kahler manifold we also construct the noncommutative version of the s 1 principal bundle over a quantizable weyl manifold

a unified algebraic approach to the classical yang baxter equation in this paper the different operator forms of the classical yang baxter equation are given in the tensor expression through a unified algebraic method it is closely related to left symmetric algebras which play an important role in many fields in mathematics and mathematical physics by studying the relations between left symmetric algebras and the classical yang baxter equation we can construct left symmetric algebras from certain classical r matrices and conversely there is a natural classical r matrix constructed from a left symmetric algebra which corresponds to a parakahler structure in geometry moreover the former in a special case gives an algebraic interpretation of the left symmetry as a lie bracket left twisted by a classical r matrix

group theoretical basis of some identities for the generalized hypergeometric series it is shown that thomae s identity between two 3f2 hypergeometric series of unit argument together with the trivial invariance under separate permutations of numerator and denominator parameters implies that the symmetric group s5 is an invariance group of this series a similar result is proved for the terminating saalschutzian 4f3 series where s6 is shown to be the invariance group of this series or s5 if one parameter is eliminated by using the saalschutz condition here bailey s identity is realized as a permutation of appropriately defined parameters finally the set of three term relations between 3f2 series of unit argument discovered by thomae j thomae j reine angew math 87 26 1879 and systematized by whipple f j whipple proc london math soc 23 104 1925 is shown to be transformed into itself under the action of the group s6 where is a two element group the 12 left cosets of s6 with respect to the invariance group s5 are the structural elements underlying the three

convergence of the wick star product we construct a frechet space as a subspace of c omega mathbb c n where the wick star product converges and is continuous the resulting frechet algebra mathcal a is studied in detail including a representation of mathcal a in the bargmann fock space and a discussion of star exponentials and coherent states

the n policy for an unreliable server with delaying repair and two phases of service this paper deals with an m x g 1 with an additional second phase of optional service and unreliable server which consist of a breakdown period and a delay period under n policy while the server is working with any phase of service it may break down at any instant and the service channel will fail for a short interval of time further concept of the delay time is also introduced if no customer arrives during the breakdown period the server becomes idle in the system until the queue size builds up to a threshold value n 1 as soon as the queue size becomes at least n the server immediately begins to serve the first phase of regular service to all the waiting customers after the completion of which only some of them receive the second phase of the optional service we derive the queue size distribution at a random epoch and departure epoch as well as various system performance measures finally we derive a simple procedure to obtain optimal stationary policy under a suitable linear cost structure

formal symplectic groupoid of a deformation quantization we give a self contained algebraic description of a formal symplectic groupoid over a poisson manifold m to each natural star product on m we then associate a canonical formal symplectic groupoid over m finally we construct a unique formal symplectic groupoid with separation of variables over an arbitrary kahler poisson manifold

quantization of kahler manifolds ii we use berezin s dequantization procedure to define a formal product on a dense subalgebra of the algebra ofsmooth functions on a compact homogeneous kahler manifold m we prove that this formal product isconvergent when m isa hermitian symmetric space 1993 american mathematical society

bilinear forms on fermionic novikov algebras novikov algebras were introduced in connection with the poisson brackets of hydrodynamic type and hamiltonian operators in formal variational calculus fermionic novikov algebras correspond to a certain hamiltonian super operator in a super variable in this paper we show that there is a remarkable geometry on fermionic novikov algebras with non degenerate invariant symmetric bilinear forms which we call pseudo riemannian fermionic novikov algebras they are related to pseudo riemannian lie algebras furthermore we obtain a procedure to classify pseudo riemannian fermionic novikov algebras as an application we give the classification in dimension 4 motivated by the one in dimension 4 we construct some examples in high dimensions

symmetry groups of bailey s transformations for 10 φ 9 series although most of the symmetry groups or invariance groups associated with two term transformations between basic hypergeometric series have been studied and identified this is not the case for the most general transformation formulae in the theory of basic hypergeometric series namely bailey s transformations for f910 series first we show that the invariance group for both bailey s two term transformations for terminating f910 series and bailey s four term transformations for non terminating f910 series rewritten as a two term transformation of a so called f series is isomorphic to the weyl group of type e 6 we continue our recent research concerning the group structure underlying three term transformations s lievens j van der jeugt invariance groups of three term transformations for basic hypergeometric series j comput appl math 197 2006 1 14 and demonstrate that the group associated with a three term transformation between these f series each admitting bailey s two term transformation is the weyl group of type e 7 we do this by giving a description of the root system of type e 7 that allows to find a transformation between equivalent three term identities in an easy way a computation shows that there are five essentially different three term transformations between these f series we give an explicit form of each of these five transformations in an elegant way to our knowledge only one of these transformations has appeared in the literature

the classification of novikov algebras in low dimensions invariant bilinear forms in this note we give a complete classification of the non degenerate symmetric invariant bilinear forms on novikov algebras in dimension 2 and 3 which can be regarded as an addendum of the classification of novikov algebras in low dimensions given in our previous work bai c m and meng d j 2001 j phys a math gen 34 1581 94

symmetric novikov superalgebras we study novikov superalgebras with nondegenerate associative supersymmetric bilinear forms which are called symmetric novikov superalgebras we show that novikov symmetric superalgebras are associative superalgebras with additional condition several examples of symmetric novikov superalgebras are included in particular examples of symmetric novikov superalgebras which are not 2 nilpotent finally we introduce some notions of double extensions in order to give inductive descriptions of symmetric novikov superalgebras

pseudo riemannian novikov algebras novikov algebras were introduced in connection with the poisson brackets of hydrodynamic type and hamiltonian operators in formal variational calculus pseudo riemannian novikov algebras denote novikov algebras with nondegenerate invariant symmetric bilinear forms in this paper we find that there is a remarkable geometry on pseudo riemannian novikov algebras and give a special class of pseudo riemannian novikov algebras

novikov algebras with associative bilinear forms novikov algebras were introduced in connection with the poisson brackets of hydrodynamic type and hamiltonian operators in formal variational calculus the goal of this paper is to study novikov algebras with non degenerate associative symmetric bilinear forms which we call quadratic novikov algebras based on the classification of solvable quadratic lie algebras of dimension not greater than 4 and novikov algebras in dimension 3 we show that quadratic novikov algebras up to dimension 4 are commutative furthermore we obtain the classification of transitive quadratic novikov algebras in dimension 4 but we find that not every quadratic novikov algebra is commutative and give a non commutative quadratic novikov algebra in dimension 6

on simple novikov algebras and their irreducible modules abstract we give a complete classification of finite dimensional simple novikov algebras and their irreducible modules over an algebraically closed field with prime characteristic moreover we introduce novikov poisson algebras and their tensor theory our tensor theory enables us to understand better certain finite dimensional simple novikov algebras and their irreducible modules

technical note mean drifts and the non ergodicity of markov chains an important question in stochastic modeling is whether or not a denumerable state markov chain is ergodic we extend a result of kaplan giving a condition for the non ergodicity of a chain based on its drifts we also clarify the condition under which the mean drift in the stationary chain is zero

weighted bergman kernels and quantization let be a bounded pseudoconvex domain in c n two positive functions on such that log log are plurisubharmonic and z a point at which log is smooth and strictly plurisubharmonic we show that as k the bergman kernels with respect to the weights k have an asymptotic expansion for x y near z where x y is an almost analytic extension of phi x x x and similarly for further if in addition is of finite type behave reasonably at the boundary and log log are strictly plurisubharmonic on we obtain also an analogous asymptotic expansion for the berezin transform and give applications to the berezin quantization finally for smoothly bounded and strictly pseudoconvex and a smooth strictly plurisubharmonic defining function for we also obtain results on the berezin toeplitz quantization

identification of berezin toeplitz deformation quantization we give a complete identification of the deformation quantization which was obtained from the berezin toeplitz quantization on an arbitrary compact kahler manifold the deformation quantization with the opposite star product proves to be a differential deformation quantization with separation of variables whose dassifying form is explicitly calculated its characteristic dass which dassifies star products up to equivalence is obtained the proof is based on the microlocal description of the szego kernel of a strictly pseudoconvex domain given by boutet de monvel and sjostrand

hom novikov algebras we study a twisted generalization of novikov algebras called hom novikov algebras in which the two defining identities are twisted by a linear map it is shown that hom novikov algebras can be obtained from novikov algebras by twisting along any algebra endomorphism all algebra endomorphisms on complex novikov algebras of dimensions 2 or 3 are computed and their associated hom novikov algebras are described explicitly another class of hom novikov algebras is constructed from hom commutative algebras together with a derivation generalizing a construction due to dorfman and gel fand two other classes of hom novikov algebras are constructed from hom lie algebras together with a suitable linear endomorphism generalizing a construction due to bai and meng

explicit formulas for noncommutative deformations of cpn and chn we give explicit expressions of a deformation quantization with separation of variables for cpn and chn this quantization method is one of the ways to perform a deformation quantization of kahler manifolds which is introduced by karabegov star products are obtained as explicit formulas in all order in the noncommutative parameter we also give the fock representations of the noncommutative cpn and chn

on free gelfand dorfman novikov poisson algebras and a pbw theorem abstract in 1997 x xu 18 19 invented a concept of novikov poisson algebras we call them gelfand dorfman novikov poisson gdn poisson algebras we construct a linear basis of a free gdn poisson algebra we define a notion of a special gdn poisson admissible algebra based on x xu s definition and an s i gelfand s observation see 9 it is a differential algebra with two commutative associative products and some extra identities we prove that any gdn poisson algebra is embeddable into its universal enveloping special gdn poisson admissible algebra also we prove that any gdn poisson algebra with the identity x y z x y z x z y is isomorphic to a commutative associative differential algebra

pseudo kahler lie algebras with abelian complex structures we study lie algebras endowed with an abelian complex structure which admit a symplectic form compatible with the complex structure we prove that each of those lie algebras is completely determined by a pair u h where u is a complex commutative associative algebra and h is a sesquilinear hermitian form on u which verifies certain compatibility conditions with respect to the associative product on u the riemannian and ricci curvatures of the associated pseudo kahler metric are studied and a characterization of those lie algebras which are einstein but not ricci flat is given it is seen that all pseudo kahler lie algebras can be inductively described by a certain method of double extensions applied to the associated complex associative commutative algebras

invariance groups of three term transformations for basic hypergeometric series the study of invariance groups associated with two term transformations between basic hypergeometric series has received its fair share of attention and indeed for most two term transformations between basic hypergeometric series the underlying invariance group is explicitly known in this article we study the group structure underlying some three term transformation formulae thereby giving an explicit and simple realization that is helpful in determining whether two of these transformation formulae are equivalent or not

stochastic decompositions in the m g 1 queue with generalized vacations this paper considers a class of m g 1 queueing models with a server who is unavailable for occasional intervals of time as has been noted by other researchers for several specific models of this type the stationary number of customers present in the system at a random point in time is distributed as the sum of two or more independent random variables one of which is the stationary number of customers present in the standard m g 1 queue i e the server is always available at a random point in time in this paper we demonstrate that this type of decomposition holds in fact for a very general class of m g 1 queueing models the arguments employed are both direct and intuitive in the course of this work moreover we obtain two new results that can lead to remarkable simplifications when solving complex m g 1 queueing models

the automorphisms of novikov algebras in low dimensions novikov algebras were introduced in connection with poisson brackets of hydrodynamic type and hamiltonian operators in the formal variational calculus they also correspond to a class of vertex algebras an automorphism of a novikov algebra is a linear isomorphism satisfying xy x y which keeps the algebraic structure the set of automorphisms of a novikov algebra is a lie group whose lie algebra is just the novikov algebra s derivation algebra the theory of automorphisms plays an important role in the study of novikov algebras in this paper we study the automorphisms of novikov algebras we get some results on their properties and classification in low dimensions these results are fundamental in a certain sense and they will serve as a guide for further development moreover we apply these results to classify gel fand dorfman bialgebras and novikov poisson algebras these results also can be used to study certain phase spaces and geometric classical r matrices

on the realization of transitive novikov algebras novikov algebras were introduced in connection with the poisson brackets of hydrodynamic type and hamiltonian operators in the formal variational calculus it is well known that the radical of a finite dimensional novikov algebra is transitive in this paper we prove that a kind realization of novikov algebras given by s gel fand is transitive and we give a deformation theory of novikov algebras in two and three dimensions we find that all transitive novikov algebras can be realized as the novikov algebras given by s gel fand and their compatible infinitesimal deformations