moyal quantization of 2 1 dimensional galilean systems stratonovich weyl kernels are constructed for some of the coadjoint orbits of the two dimensional extended galilean group g 2 1 as an intermediate step the unitary irreducible representations associated with a given group orbit are obtained by using the kirillov mackey theory star products are defined in the sense of moyal for functions on each of these orbits the central extension of g 2 1 with parameter k is also analyzed which results from the commutator between the generators of boosts to conclude that it originates a sort of nonrelativistic remainder of the thomas precession

the frobenius semiradical of a lie algebra univ limburg dept math b 3590 diepenbeek belgium ooms ai univ limburg dept math univ campus b 3590 diepenbeek belgium alfons ooms luc ac be

a modified fuzzy c means algorithm for bias field estimation and segmentation of mri data we present a novel algorithm for fuzzy segmentation of magnetic resonance imaging mri data and estimation of intensity inhomogeneities using fuzzy logic mri intensity inhomogeneities can be attributed to imperfections in the radio frequency coils or to problems associated with the acquisition sequences the result is a slowly varying shading artifact over the image that can produce errors with conventional intensity based classification our algorithm is formulated by modifying the objective function of the standard fuzzy c means fcm algorithm to compensate for such inhomogeneities and to allow the labeling of a pixel voxel to be influenced by the labels in its immediate neighborhood the neighborhood effect acts as a regularizer and biases the solution toward piecewise homogeneous labelings such a regularization is useful in segmenting scans corrupted by salt and pepper noise experimental results on both synthetic images and mr data are given to demonstrate the effectiveness and efficiency of the proposed algorithm

locally finite simple weight modules over twisted generalized weyl algebras abstract we present methods and explicit formulas for describing simple weight modules over twisted generalized weyl algebras when a certain commutative subalgebra is finitely generated over an algebraically closed field we obtain a classification of a class of locally finite simple weight modules as those induced from simple modules over a subalgebra isomorphic to a tensor product of noncommutative tori as an application we describe simple weight modules over the quantized weyl algebra

fuzzy c means clustering with local information and kernel metric for image segmentation in this paper we present an improved fuzzy c means fcm algorithm for image segmentation by introducing a tradeoff weighted fuzzy factor and a kernel metric the tradeoff weighted fuzzy factor depends on the space distance of all neighboring pixels and their gray level difference simultaneously by using this factor the new algorithm can accurately estimate the damping extent of neighboring pixels in order to further enhance its robustness to noise and outliers we introduce a kernel distance measure to its objective function the new algorithm adaptively determines the kernel parameter by using a fast bandwidth selection rule based on the distance variance of all data points in the collection furthermore the tradeoff weighted fuzzy factor and the kernel distance measure are both parameter free experimental results on synthetic and real images show that the new algorithm is effective and efficient and is relatively independent of this type of noise

an algebraic slice in the coadjoint space of the borel and the coxeter element abstract let g be a complex simple lie algebra and b a borel subalgebra the algebra y of polynomial semi invariants on the dual b of b is a polynomial algebra on rank g generators grothendieck and dieudonne 1965 1967 16 the analogy with the semisimple case suggests there exists an algebraic slice to coadjoint action that is an affine translate y v of a vector subspace of b such that the restriction map induces an isomorphism of y onto the algebra r y v of regular functions on y v this holds in type a and even extends to all biparabolic subalgebras joseph 2007 20 but the construction fails in general even with respect to the borel moreover already in type c 2 no algebraic slice exists very surprisingly the exception of type c 2 is itself an exception indeed an algebraic slice for the coadjoint action of the borel subalgebra is constructed for all simple lie algebras except those of types b 2 m c n and f 4 outside type a the slice obtained meets an open dense subset of regular orbits even though the special point y of the slice is not itself regular this explains the failure of our previous construction

field of fractions of certain quantum algebras abstract in this paper we show that the field of fractions of certain algebras appearing in the theory of quantum groups are isomorphic to the field of fractions of quantum n space when the parameter q is not a root of 1 more precisely the quantum serre relations of type a n and the relations defining the quantum weyl algebra induce q communtation relations in the field of fractions also we study the problem of separation of these skew fields using the standard embeddings in non commutative series

an extension of the standard mixture model for image segmentation standard gaussian mixture modeling gmm is a well known method for image segmentation however the pixels themselves are considered independent of each other making the segmentation result sensitive to noise to reduce the sensitivity of the segmented result with respect to noise markov random field mrf models provide a powerful way to account for spatial dependences between image pixels however their main drawback is that they are computationally expensive to implement and require large numbers of parameters based on these considerations we propose an extension of the standard gmm for image segmentation which utilizes a novel approach to incorporate the spatial relationships between neighboring pixels into the standard gmm the proposed model is easy to implement and compared with mrf models requires lesser number of parameters we also propose a new method to estimate the model parameters in order to minimize the higher bound on the data negative log likelihood based on the gradient method experimental results obtained on noisy synthetic and real world grayscale images demonstrate the robustness accuracy and effectiveness of the proposed model in image segmentation as compared to other methods based on standard gmm and mrf models

the projective unitary irreducible representations of the poincare group in 1 2 dimensions a complete analysis is given of the projective unitary irreducible representations of the poincare group in 1 2 dimensions applying the mackey theorem and using an explicit formula for the universal covering group of the lorentz group in 1 2 dimensions explicit formulas are given for all representations

relativistic field theories in three dimensions we provide a complete classification of the unitary irreducible representations of the 2 1 dimensional poincare group we show in particular that only two types of spin are available for massless field theories we also construct generalized foldy wouthuysen transformations which connect the physical uir s with covariant field theories in three dimensions

unitary representations of the 4 1 de sitter group on irreducible representation spaces of the poincare group the construction of the principal continuous series of unitary representations of the simply connected covering group of the 4 1 de sitter group on unitary irreducible representation spaces of the poincare group is presented a unitary irreducible representation space of this covering group of the de sitter group is realized as the direct sum of two irreducible representation spaces of the poincare group possible physical implications are indicated in particular an interpretation of the instantaneous velocity operator in the dirac theory as the spin part of the de sitter boosts is given we obtain a simple method of computing the matrix elements of the generators of the de sitter group in an so 4 basis using the matrix elements of the generators of the four dimensional euclidean group also we obtain explicit expressions for certain matrix elements between the spinor and so 4 basis of the representation space as functions on the coset space so 4 so 3

effacement des derivations et spectres premiers des algebres quantiques abstract given any commutative field k and any iterated ore extension r k x1 x2 2 2 xn n n satisfying some suitable assumptions we construct the so called derivative elimination algorithm it consists of a sequence of changes of variables inside the division ring f fract r starting with the indeterminates x1 xn and terminating with new variables t1 tn these new variables generate some quantum affine space r such that f fract r this algorithm induces a natural embedding spec r spec r which satisfies the following property if p is in spec r then fract r p fract r p we study both the derivative elimination algorithm and natural embedding and use them to produce for the general case a common proof of the quantum gelfand kirillov property for the prime homomorphic images of the following quantum algebras u q w g b q w g w w r q g where g denotes any complex semi simple connected simply connected lie group with associated lie algebra g and weyl group w quantum matrices algebras quantum weyl algebras and quantum euclidean respectively symplectic spaces another application will be given in g cauchon j algebra to appear in the general case the prime spectrum of any quantum matrices algebra satisfies the normal separation property

grafting and poisson structure in 2 1 gravity with vanishing cosmological constant we relate the geometrical construction of 2 1 spacetimes via grafting to phase space and poisson structure in the chern simons formulation of 2 1 dimensional gravity with vanishing cosmological constant on manifolds of topology mathbb r times s g where sg is an orientable two surface of genus g 1 we show how grafting along simple closed geodesics is implemented in the chern simons formalism and derive explicit expressions for its action on the holonomies of general closed curves on sg we prove that this action is generated via the poisson bracket by a gauge invariant observable associated to the holonomy of we deduce a symmetry relation between the poisson brackets of observables associated to the lorentz and translational components of the holonomies of general closed curves on sg and discuss its physical interpretation finally we relate the action of grafting on the phase space to the action of dehn twists and show that grafting can be viewed as a dehn twist with a formal parameter satisfying 2 0

connected graded hopf algebras we study algebraic and homological properties of two classes of infinite dimensional hopf algebras over an algebraically closed field k of characteristic zero the first class consists of those hopf k algebras that are connected graded as algebras and the second class are those hopf k algebras that are connected as coalgebras for many but not all of the results presented here the hopf algebras are assumed to have finite gel fand kirillov dimension it is shown that if the hopf algebra h is a connected graded hopf algebra of finite gel fand kirillov dimension n then h is a noetherian domain which is cohen macaulay artin schelter regular and auslander regular of global dimension n it has s2 idh and is calabi yau detailed information is also provided about the hilbert series of h our results leave open the possibility that the first class of algebras is properly contained in the second for this second class the hopf k algebras of finite gel fand kirillov dimension n with connected coalgebra the underlying coalgebra is shown to be artin schelter regular of global dimension n both these classes of hopf algebra share many features in common with enveloping algebras of finite dimensional lie algebras for example an algebra in either of these classes satisfies a polynomial identity only if it is a commutative polynomial algebra nevertheless we construct as one of our main results an example of a hopf k algebra h of gel fand kirillov dimension 5 which is connected graded as an algebra and connected as a coalgebra but is not isomorphic as an algebra to u g for any lie algebra g

ray representations of n 2 1 dimensional galilean group for a quantum mechanical system modeled via unitary or antiunitary representations of a symmetry group g with lie algebra g the hamiltonian h is of special interest if h is an element of g or of the universal enveloping algebra u g a generic time dependence for any element in u g is given through the heisenberg picture as an example we consider a system with gal n as symmetry group with h as one of the generators for n 3 one gets from ray representations the free schrodinger equation for n 1 a peculiarity occurs the free equation has an interaction term which results from the construction and parametrization of unitary ray representations for n 2 there is another special feature there exist ray representations of the universal covering group gal 2 which induce no ray representations of gal 2 furthermore for these representations it is not possible to construct a schrodinger equation

segmentation of brain mr images through a hidden markov random field model and the expectation maximization algorithm the finite mixture fm model is the most commonly used model for statistical segmentation of brain magnetic resonance mr images because of its simple mathematical form and the piecewise constant nature of ideal brain mr images however being a histogram based model the fm has an intrinsic limitation no spatial information is taken into account this causes the fm model to work only on well defined images with low levels of noise unfortunately this is often not the the case due to artifacts such as partial volume effect and bias field distortion under these conditions fm model based methods produce unreliable results here the authors propose a novel hidden markov random field hmrf model which is a stochastic process generated by a mrf whose state sequence cannot be observed directly but which can be indirectly estimated through observations mathematically it can be shown that the fm model is a degenerate version of the hmrf model the advantage of the hmrf model derives from the way in which the spatial information is encoded through the mutual influences of neighboring sites although mrf modeling has been employed in mr image segmentation by other researchers most reported methods are limited to using mrf as a general prior in an fm model based approach to fit the hmrf model an em algorithm is used the authors show that by incorporating both the hmrf model and the em algorithm into a hmrf em framework an accurate and robust segmentation can be achieved more importantly the hmrf em framework can easily be combined with other techniques as an example the authors show how the bias field correction algorithm of guillemaud and brady 1997 can be incorporated into this framework to achieve a three dimensional fully automated approach for brain mr image segmentation

solution of a q difference noether problem and the quantum gelfand kirillov conjecture for mathfrak gl _n it is shown that the q difference noether problem for all classical weyl groups has a positive solution simultaneously generalizing well known results on multisymmetric functions of mattuck proc am math soc 19 764 765 1968 and miyata nagoya math j 41 69 73 1971 in the case q 1 and q deforming the noncommutative noether problem for the symmetric group futorny et al in adv math 223 773 796 2010 it is also shown that the quantum gelfand kirillov conjecture for mathfrak gl n for a generic q follows from the positive solution of the q difference noether problem for the weyl group of type d n the proof is based on the theory of galois rings futorny and ovsienko in j algebra 324 598 630 2010 from here we obtain a proof of the quantum gelfand kirillov conjecture for mathfrak gl n and for a certain extension of mathfrak sl n previously the case of mathfrak sl n was shown by fauquant millet j algebra 218 93 116 1999 and by alev and dumas j algebra 170 229 265 1994 for n 2 3 moreover we give an explicit description of the skew fields of fractions for u q mathfrak gl n and u q mathrm ext mathfrak sl n which generalizes the results of alev and dumas j algebra 170 229 265 1994

algebra of derivations of lie algebras abstract we show a method to determine the space of derivations of any lie algebra and in particular we apply this method to a special class of lie algebras those nilpotent with low nilindex most calculations have been supported by the software mathematica 3 0

modular lie algebras and the gelfand kirillov conjecture let mathfrak g be a finite dimensional simple lie algebra over an algebraically closed field mathbb k of characteristic 0 let mathfrak g mathbb z be a chevalley form of mathfrak g and mathfrak g bbbk mathfrak g mathbb z otimes mathbb z bbbk where bbbk is the algebraic closure of mathbb f p let g bbbk be a simple simply connected algebraic bbbk group with operatorname lie g bbbk mathfrak g bbbk in this paper we apply recent results of rudolf tange on the fraction field of the centre of the universal enveloping algebra u mathfrak g bbbk to show that if the gelfand kirillov conjecture from 1966 holds for mathfrak g then for all p 0 the field of rational functions bbbk mathfrak g bbbk is purely transcendental over its subfield bbbk mathfrak g bbbk g bbbk very recently it was proved by colliot thelene kunyavski popov and reichstein that the field of rational functions mathbb k mathfrak g is not purely transcendental over its subfield mathbb k mathfrak g mathfrak g if mathfrak g is of type b n n 3 d n n 4 e6 e7 e8 or f4 we prove a modular version of this result valid for p 0 and use it to show that in characteristic 0 the gelfand kirillov conjecture fails for the simple lie algebras of the above types in other words if mathfrak g is of type b n n 3 d n n 4 e6 e7 e8 or f4 then the lie field of mathfrak g is more complicated than expected

the polynomiality of the poisson center and semi center of a lie algebra and dixmier s fourth problem abstract let g be a finite dimensional lie algebra over an algebraically closed field k of characteristic zero we provide necessary and also some sufficient conditions in order for its poisson center and semi center to be polynomial algebras over k this occurs for instance if g is quadratic of index 2 with g g g and also if g is nilpotent of index at most 2 the converse holds for filiform lie algebras of type l n q n r n and w n we show how dixmier s fourth problem for an algebraic lie algebra g can be reduced to that of its canonical truncation g moreover dixmier s statement holds for all lie algebras of dimension at most eight the nonsolvable ones among them possess a polynomial poisson center and semi center

enveloping algebras of simple three dimensional lie algebras abstract the killing form of a simple three dimensional lie algebra is shown to classify the lie algebra and its enveloping algebra the lie algebra is isomorphic to the two by two trace zero matrices the so called split case if and only if the form is isotropic in the sense of quadratic form theory in characteristic zero the skew field of quotients of the enveloping algebra is shown to be isomorphic to a weyl skew field if and only if the lie algebra is split automorphisms of the lie algebra and its enveloping algebra are induced by isometries of the killing form in the nonsplit case

filtrations on simple artinian rings abstract filtrations on simple artinian rings are related to pseudo valuations by conditions on the associated graded rings

central extensions of the quasi orthogonal lie algebras we determine the central extensions of a whole family of lie algebras obtained by the method of graded contractions from n arbitrary all the inhomogeneous orthogonal and pseudo orthogonal algebras are members of this family as well as a large number of other non semisimple algebras all of which have at least a semidirect structure in some cases two or more the dimensions of their second cohomology groups and the explicit expression of their central extensions are given

on the statistical analysis of dirty pictures may 7th 1986 professor a f m smith in the chair summary a continuous two dimensional region is partitioned into a fine rectangular array of sites or pixels each pixel having a particular colour belonging to a prescribed finite set the true colouring of the region is unknown but associated with each pixel there is a possibly multivariate record which conveys imperfect information about its colour according to a known statistical model the aim is to reconstruct the true scene with the additional knowledge that pixels close together tend to have the same or similar colours in this paper it is assumed that the local characteristics of the true scene can be represented by a nondegenerate markov random field such information can be combined with the records by bayes theorem and the true scene can be estimated according to standard criteria however the computational burden is enormous and the reconstruction may reflect undesirable largescale properties of the random field thus a simple iterative method of reconstruction is proposed which does not depend on these large scale characteristics the method is illustrated by computer simulations in which the original scene is not directly related to the assumed random field some complications including parameter estimation are discussed potential applications are mentioned briefly

quantification de la localisation de dixmier de u sln 1 c resume in this article we extend to the quantum case the classical result of dixmier according to which up to localization the enveloping algebra of sl n 1 c is a central polynomial extension of the enveloping algebra of some parabolic subalgebra in fact the latter has a semiinvariant element d by which it is sufficient to localize to obtain the result the methods we use here are quite different from those used by dixmier indeed in the quantum case the powers of the indeterminate q would make calculations similar to those of dixmier much too complicated on the other hand when we use the rosso form which allows us to work in the hopf dual of q sl n 1 c the calculations become much easier than they would be in q sl n 1 c

an embedding of the poincare lie algebra into an extension of the lie field of so0 1 4 the isomorphism between algebraic extensions of the lie fields of so0 1 4 and the poincare group are considered herein it is shown that the principal series of unitary ray representations of so0 1 4 are associated via the isomorphism with real mass positive and negative energy representations of the poincare lie algebra with arbitrary spin results on the most degenerate exceptional series of so0 1 4 representations are also given

on commutative polarizations let l be a finite dimensional lie algebra over a field k of characteristic zero and let u l be its enveloping algebra with quotient division ring d l let p be a commutative lie subalgebra of l in o2 the necessary and sufficient condition on p was given in order for d p to be a maximal commutative subfield of d l in particular this condition is satisfied if p is a commutative polarization cp with respect to any regular f l and the converse holds if l is ad algebraic the purpose of this paper is to study lie algebras admitting these cp s and to demonstrate their widespread occurrence first we have the following characterisation if l is completely solvable p is a cp of l if and only if there exists a descending chain of lie subalgebras

a quadratic poisson gel fand kirillov problem in prime characteristic the quadratic poisson gel fand kirillov problem asks whether the field of fractions of a poisson algebra is poisson birationally equivalent to a poisson affine space i e to a polynomial algebra k x1 xn with poisson bracket defined by xi xj ijxixj for some skew symmetric matrix ij mn k this problem was studied in 9 over a field of characteristic 0 by using a poisson version of the deleting derivation homomorphism of cauchon in this paper we study the quadratic poisson gel fand kirillov problem over a field of arbitrary characteristic in particular we prove that the quadratic poisson gel fand kirillov problem is satisfied for a large class of poisson algebras arising as semiclassical limits of quantised coordinate rings for we introduce the concept of higher poisson derivation which allows us to extend the poisson version of the deleting derivation homomorphism from the characteristic 0 case to the case of arbitrary characteristic when a torus is acting rationally by poisson automorphisms on a poisson polynomial algebra arising as the semiclassical limit of a quantised coordinate ring we prove under some technical assumptions that quotients by poisson prime torus invariant ideals also satisfy the quadratic poisson gel fand kirillov problem in particular we show that coordinate rings of determinantal varieties satisfy the quadratic poisson gel fand kirillov problem

rough sets and stomped normal distribution for simultaneous segmentation and bias field correction in brain mr images the segmentation of brain mr images into different tissue classes is an important task for automatic image analysis technique particularly due to the presence of intensity inhomogeneity artifact in mr images in this regard this paper presents a novel approach for simultaneous segmentation and bias field correction in brain mr images it integrates judiciously the concept of rough sets and the merit of a novel probability distribution called stomped normal sn distribution the intensity distribution of a tissue class is represented by sn distribution where each tissue class consists of a crisp lower approximation and a probabilistic boundary region the intensity distribution of brain mr image is modeled as a mixture of finite number of sn distributions and one uniform distribution the proposed method incorporates both the expectation maximization and hidden markov random field frameworks to provide an accurate and robust segmentation the performance of the proposed approach along with a comparison with related methods is demonstrated on a set of synthetic and real brain mr images for different bias fields and noise levels

the gelfand kirillov conjecture for semi direct products of lie algebras let g be an n dimensional lie algebra over a field k of characteristic zero and let w be a g module such that dimw n sufficient conditions are given in order for the semi direct product g w to satisfy the gelfand kirillov conjecture this implies that this conjecture holds for an important class of frobenius lie algebras special attention is devoted to the case where g sl 2 k

rough sets for bias field correction in mr images using contraharmonic mean and quantitative index one of the challenging tasks for magnetic resonance mr image analysis is to remove the intensity inhomogeneity artifact present in mr images which often degrades the performance of an automatic image analysis technique in this regard the paper presents a novel approach for bias field correction in mr images it judiciously integrates the merits of rough sets and contraharmonic mean while the contraharmonic mean is used in low pass averaging filter to estimate the bias field in multiplicative model the concept of lower approximation and boundary region of rough sets deals with vagueness and incompleteness in filter structure definition a theoretical analysis is presented to justify the use of both rough sets and contraharmonic mean for bias field estimation the integration enables the algorithm to estimate optimum or near optimum bias field some new quantitative indexes are introduced to measure intensity inhomogeneity artifact present in a mr image the performance of the proposed approach along with a comparison with other approaches is demonstrated on both simulated and real mr images for different bias fields and noise levels

parameter estimation and tissue segmentation from multispectral mr images a statistical method is developed to classify tissue types and to segment the corresponding tissue regions from relaxation time t sub 1 t sub 2 and proton density p sub d weighted magnetic resonance images the method assumes that the distribution of image intensities associated with each tissue type can be expressed as a multivariate likelihood function of three weighted signal intensity values t sub 1 t sub 2 p sub d at each location within that tissue regions the method further assumes that the underlying tissue regions are piecewise contiguous and can be characterized by a markov random field prior in classifying the tissue types the method models the likelihood of realizing the images as a finite multivariate mixture function the class parameters associated with the tissue types i e the weighted intensity means variances and correlation coefficients of the multivariate function as well as the number of voxels within regions of the tissue types of are estimated by maximum likelihood the estimation fits the class parameters to the image data via the expectation maximization algorithm the number of classes associated with the tissue types is determined by the information criterion of minimum description length the method segments the tissue regions given the estimated class parameters by maximum a posteriori probability the prior is constructed by the tissue region membership of the first and second order neighborhood the method is tested by a few sets of t sub 1 t sub 2 and p sub d weighted images of the brain acquired with a 1 5 tesla whole body scanner the number of classes and the associated class parameters are automatically estimated the regions of different brain tissues are satisfactorily segmented

gell mann formula for simple complex lie groups and geometric quantization a lie poisson isomorphism for lie algebras g and q k k is derived in a closed form where g is complex and simple and k is the maximal compact subalgebra in g this isomorphism enables one to find a generalized gell mann formula relating unitary irreducible representations of the corresponding lie groups g and q the case g sl n c k su n is considered in detail a simple relation between characters is obtained

galois orders in skew monoid rings abstract we introduce a new class of noncommutative rings galois orders realized as certain subrings of invariants in skew semigroup rings and develop their structure theory the class of galois orders generalizes classical orders in noncommutative rings and contains many important examples such as the generalized weyl algebras the universal enveloping algebra of the general linear lie algebra associated yangians and finite w algebras

stomped t a novel probability distribution for rough probabilistic clustering abstract rough clustering is one of the principal research areas in data mining machine learning pattern recognition and bioinformatics among different variants of rough clustering rough probabilistic clustering is a new concept introduced recently in rough probabilistic clustering a class is defined as the union of two disjoint regions namely a crisp lower approximation region and a probabilistic boundary region in this regard stomped normal sn distribution provides a statistical modeling of the data set in rough probabilistic clustering framework the sn distribution models the central tendency dispersion and width of the lower approximation region of each class using its mean variance and width parameter respectively however it does not take into consideration the property of kurtosis of the class distribution which controls the concentration of values around mean and shape of the tail of data distribution in this background a novel probability distribution named stomped t s t distribution is introduced in the paper for rough probabilistic clustering the proposed probability distribution incorporates the property of kurtosis into the sn framework the proposed s t probability distribution is then integrated within the rough probabilistic clustering framework for precise and robust clustering of the data the efficacy of the proposed clustering algorithm is demonstrated for unsupervised data clustering and image segmentation problems along with a comparative performance analysis with related algorithms

gelfand kirillov conjecture in positive characteristics abstract let g be a finite dimensional lie algebra over an algebraically closed field of characteristic p 0 and let u g be the universal enveloping algebra of g we show in this paper that the division ring of fractions of u g is isomorphic to the ring of fractions of a weyl algebra in the following cases for g gl n or sl n if p n for the witt algebra w 1 and for some tensor product w 1 a of w 1 with a truncated polynomial ring furthermore we also show that the centre of u g in the last two cases is a unique factorisation domain in accordance with recent results of premet tange braun and hajarnavis

the gelfand kirillov conjecture for lie algebras of dimension at most eight univ reims dept math f 51687 reims 2 france univ limburg dept math b 3590 diepenbeek belgium alev j univ reims dept math bp 1039 f 51687 reims 2 france

construction of representations of poincare group using lie fields in this paper we give an explicit construction of the unitary irreducible representations of the poincare groups in 2 3 and 4 space time dimensions on hilbert spaces associated with the schrodinger representation of the weyl algebra for n 1 2 and 3 respectively our method of constructing the representations uses extension and localization of the enveloping algebras associated with these weyl algebras and the poincare algebras

a class of counterexamples to the gel fand kirillov conjecture limburgs univ centrum dept wni b 3500 diepenbeek belgium alev j univ reims ufr sci dept math moulin housse bp 347 f 51062 reims france

computing invariants and semi invariants by means of frobenius lie algebras abstract let u be the enveloping algebra of a finite dimensional lie algebra over a field k of characteristic zero z u its center and sz u its semi center a sufficient condition is given in order for sz u to be a polynomial algebra over k surprisingly this condition holds for many lie algebras especially among those for which the radical is nilpotent in which case sz u z u in particular it allows the explicit description of z u for more than half of all complex indecomposable nilpotent lie algebras of dimension at most 7

the gelfand kirillov conjecture and gelfand tsetlin modules for finite w algebras abstract we address two problems with the structure and representation theory of finite w algebras associated with general linear lie algebras finite w algebras can be defined using either kostant s whittaker modules or a quantum hamiltonian reduction our first main result is a proof of the gelfand kirillov conjecture for the skew fields of fractions of finite w algebras the second main result is a parameterization of finite families of irreducible gelfand tsetlin modules using gelfand tsetlin subalgebra as a corollary we obtain a complete classification of generic irreducible gelfand tsetlin modules for finite w algebras

on certain maximal subfields in the quotient division ring of an enveloping algebra univ limburg dept math b 3590 diepenbeek belgium ooms ai univ limburg dept math b 3590 diepenbeek belgium

algebras of invariant differential operators abstract we prove that an invariant subalgebra a n w of the weyl algebra a n is a galois order over an adequate commutative subalgebra when w is a two parameters irreducible unitary reflection group g m 1 n m 1 n 1 including the weyl group of type b n or alternating group a n or the product of n copies of a cyclic group of fixed finite order earlier this was established for the symmetric group in 15 in each of the cases above except for the alternating groups we show that a n w is free as a right left module similar results are established for the algebra of w invariant differential operators on the n dimensional torus where w is a symmetric group s n or orthogonal group of type b n or d n as an application of our technique we prove the quantum gelfand kirillov conjecture for u q s l 2 the first witten deformation and the woronowicz deformation

on the integrability of certain symmetric representations of the lie algebra of so0 4 1 a proof of the existence of an essentially self adjoint extension of a symmetric so0 4 1 nelson operator which is constructed out of the generators of a positive mass arbitrary spin unitary irreducible representation of the poincare group is presented our analysis of so0 4 1 and its lie algebra provides us with an example of an observation of harish chandra there exist subspaces of the space of differentiable vectors of a representation of a noncompact group which are invariant under the lie algebra but the closures of the subspaces are not invariant under the group the chief results of this paper should hold true for so0 n 1 in particular we should have a realization of an arbitrary principal series irreducible unitary representation of so0 n 1 on the direct sum of two identical unitary irreducible representation spaces of the motion group in an n dimensional minkowski space which has one timelike dimension

fields of fractions of quantum solvable algebras abstract we introduce the notion of pure q solvable algebra the quantum matrices quantum weyl algebra u q n are the examples it is proved that the skew field of fractions of a pure q solvable algebra r is isomorphic to the skew field of twisted rational functions this is a quantum version of the gelfand kirillov conjecture for solvable algebraic lie algebras

quantum group invariants and link polynomials a general method is developed for constructing quantum group invariants and determining their eigenvalues applied to the universal matrix this method leads to the construction of a closed formula for link polynomials to illustrate the application of this formula the quantum groups uq es uq so 2m 1 and uq gl m are considered as examples and corresponding link polynomials are obtained

transitive symplectic manifolds in 1 2 dimensions a complete list of all transitive symplectic manifolds of the poincare and galilei group in 1 2 dimensions is given

on the goldie quotient ring of the enveloping algebra of a classical simple lie superalgebra abstract if g is a classical simple lie superalgebra g p n the enveloping algebra u g is a prime ring and hence has a simple artinian ring of quotients q u g by goldie s theorem we show that if g has type i then q u g is a matrix ring over q u g 0 on the other hand if g osp 1 2r then by extending the center of u g we obtain a prime ring whose goldie quotient ring is a matrix ring over the quotient division ring of a weyl algebra this is an analog of a result of gelfand and kirillov