a family of simple weight modules over the virasoro algebra abstract using simple modules over the derivation lie algebra c t d d t for the polynomial algebra c t we construct new weight modules over the witt algebra where all the weight spaces are infinite dimensional we determine the necessary and sufficient conditions for these new modules being simple as well as determining the necessary and sufficient conditions for two witt modules being isomorphic if a module is not simple we obtain all its submodules as a consequence we fully determine the simplicity and isomorphism classes for the witt modules defined by 3 which are a small proportion of the modules constructed in this study

generalized verma modules over sln 2 induced from u hn free sln 1 modules abstract a class of generalized verma modules over sl n 2 are constructed from sl n 1 modules which are u h n free modules of rank 1 the necessary and sufficient conditions for these sl n 2 modules to be simple are determined this leads to a class of new simple sl n 2 modules

some model theory over hereditary noetherian domains questions in the model theory of modules over hereditary noetherian domains are investigated with particular attention being paid to differential polynomial rings and to generalized weyl algebras we prove that there exists no isolated point in the ziegler spectrum over a simple hereditary generalized weyl algebra a of the sort considered by bavula algebra i analiz 4 1 1992 75 97 over a field k with char k 0 the first weyl algebra a 1 k is one such and the category of finite length modules over a does not have any almost split sequence we show that the theory of all modules over a wide class of generalized weyl algebras and related rings interprets the word problem for groups and in the case that the field is countable there exists a superdecomposable pure injective module over a this class includes for example the universal enveloping algebra usl 2 k

categorification of induced cell modules and the rough structure of generalised verma modules this paper presents categorifications of right cell modules and induced cell modules for hecke algebras of finite weyl groups fit type a we show that these categorifications depend only on the isomorphism class of the cell module not on the cell itself our main application is multiplicity formulas for parabolically induced modules over a reductive lie algebra of type a which finally determines the so called rough structure of generalised verma modules on the way we present several categorification results and give a positive answer to kostant s problem from a joseph kostant s problem goldie rank and the gelfand kirillov conjecture invent math 56 3 1980 191 213 in many cases we also present a general setup of decategorification precategorification and categorification

whittaker modules over virasoro like algebra in this paper we study whittaker modules over virasoro like algebra relative to some total order we determine all whittaker vectors and the irreducibilities of the universal whittaker modules for the reducible ones we determine their unique maximal submodules and the corresponding irreducible quotient modules are just those modules constructed by batra et al j algebra 322 12 4163 4180 2009 using their results we can deduce more properties on the maximal submodules and irreducible modules

krull dimension of generalized weyl algebras with noncommutative coefficients abstract we obtain formulae for the krull dimension of the generalized weyl algebra t r a where r is a left noetherian ring

continuous varying linear systems abstract we discuss implicit systems of ordinary linear differential equations with time variable coefficients their solutions in the signal space of hyperfunctions according to sato and their solution spaces called time varying linear systems or behaviours from the system theoretic point of view the basic result inspired by an analogous one for multidimensional constant linear systems is a duality theorem which establishes a categorical one one correspondence between time varying linear systems or behaviours and finitely generated modules over a suitable skew polynomial ring of differential operators this theorem is false for the signal spaces of infinitely often differentiable functions or of meromorphic hyper functions or of distributions on r it is used to obtain various results on key notions of linear system theory several new algorithms for modules over rings of differential operators and in particular new grobner basis algorithms due to insa and pauer make the system theoretic results effective

irreducible virasoro modules from irreducible weyl modules abstract we use block s results to classify irreducible modules over the differential operator algebra c t t 1 d d t from modules a over c t t 1 d d t and using the twisting technique we construct a class of modules a b over the virasoro algebra for any b c these new virasoro modules are generally not weight modules the necessary and sufficient conditions for a b to be irreducible are obtained then we determine the necessary and sufficient conditions for two such irreducible virasoro modules to be isomorphic many interesting examples for such irreducible virasoro modules with different features are provided at the end of the paper in particular the class of irreducible virasoro modules b for any c and any b c are defined on the polynomial algebra c x

fraction representations and highest weight like representations of the virasoro algebra abstract in this paper two new classes of irreducible modules over the centerless virasoro algebra v are obtained these modules are generally not weight modules or whittaker modules we first construct a class of modules over v parameterized by any 2 n 2 complex numbers for any nonnegative integer n which we call fraction modules the necessary and sufficient conditions for fraction modules to be irreducible are determined also we determine the necessary and sufficient conditions for two irreducible fraction modules to be isomorphic then we define highest weight like verma modules over v these modules behave like highest weight verma modules it is proved that each highest weight like verma module has an irreducible quotient module which is isomorphic to a subquotient of some reducible fraction module

finite dimensional simple modules over generalized heisenberg algebras abstract generalized heisenberg algebras h f for any polynomial f h c h have been used to explain various physical systems and many physical phenomena for the last 20 years in this paper we first obtain the center of h f and the necessary and sufficient conditions on f for two h f to be isomorphic then we determine all finite dimensional simple modules over h f for any polynomial f h c h more precisely there are three classes of them a h f z a b h f z a and c h f z n if f w h c for any c c and n th n 1 primitive root w of unity we actually obtain a complete classification of all irreducible modules over h f

simple restricted modules for neveu schwarz algebra abstract in this paper we give a construction of simple modules generalizing both highest weight and whittaker modules for the neveu schwarz algebra in the spirit of the work of mazorchuk and zhao on simple virasoro modules we establish a 1 1 correspondence between simple restricted neveu schwarz modules and simple modules of a family of finite dimensional solvable lie superalgebras associated to the neveu schwarz algebra moreover for two of these superalgebras all simple modules are classified

on the nullity distribution of a submanifold of a space form if m is a submanifold of a space form the nullity distribution mathcal n of its second fundamental form is when defined the common kernel of its shape operators in this paper we will give a local description of any submanifold of the euclidean space by means of its nullity distribution we will also show the following global result if m is a complete irreducible submanifold of the euclidean space or the sphere then its complementary distribution mathcal n bot is completely non integrable this means that any two points in m can be joined by a curve everywhere perpendicular to mathcal n we will finally show that this statement is false for a submanifold of the hyperbolic space

prime ideals of the enveloping algebra of the euclidean algebra and a classification of its simple weight modules a classification of the simple weight modules is given for the 6 dimensional euclidean lie algebra x1d522 3 x1d530 x1d529 2 v3 as an intermediate step a classification of all simple modules is given for the centralizer c of the cartan element h in the universal enveloping algebra x1d4b0 u x1d522 3 generators and defining relations for the algebra c are found there are three quadratic relations and one cubic relation the algebra c is a noetherian domain of gelfand kirillov dimension 5 classifications of prime primitive completely prime and maximal ideals are given for the algebra u

wild torsion modules over weyl algebras and general torsion modules over hnps let a 1 be the first weyl algebra over a field f of characteristic zero we show that the category of a 1 modules of finite length is wild despite the fact that every a 1 module of finite length is cyclic in fact the category of a 1 modules not necessarily finitely generated of socle height 2 is wild in a very strong sense among the applications we show i essentially any f algebra can occur as the endomorphism algebra of an a 1 module of socle height 2 ii a 1 has very large indecomposable modules of finite length iii there is an hnp hereditary noetherian prime ring that has indecomposable modules of finite length requiring arbitrary many generators we also complete the basic theory of finitely generated modules over general hnps by showing that every such module is a direct sum of right ideals and homomorphic images of right ideals and by proving a simultaneous decomposition theorem for an arbitrary projective module and submodule

simple sl_ n 1 module structures on u h abstract we study the category m consisting of u sl n 1 modules whose restriction to u h is free of rank 1 in particular we classify isomorphism classes of objects in m and determine their submodule structure this leads to new sl n 1 modules for n 1 we also find the central characters and derive an explicit formula for taking tensor product with a simple finite dimensional module

the injective spectrum of a right noetherian ring abstract the injective spectrum is a topological space associated to a ring r which agrees with the zariski spectrum when r is commutative noetherian we consider injective spectra of right noetherian rings and locally noetherian grothendieck categories and establish some basic topological results and a functoriality result as well as links between the topology and the krull dimension of the ring in the sense of gabriel and rentschler finally we use these results to compute a number of examples

dixmier s problem 5 for the weyl algebra abstract the purpose of this paper is to give a negative answer to problem 5 and a positive answer in the case of homogeneous elements to problem 4 of the article of j dixmier bull soc math france 96 1968 209 242 on the first weyl algebra

the simple modules of certain generalized crossed products abstract we consider a dedekind domaindand az graded ring r i z r i withr0 dand eachri dvibeing a freed module of rank 1 the structure ofris described by an automorphism ofdand a generalized 2 cocyclec z z dnot necessarily taking its values in the units ofd the aim of this paper is to classify the simpler modules say in the case wherec i j 0 for alli j z we also deal with this problem in then graded case as a consequence we obtain a description of the simple modules of some classical algebras and of generalized weyl algebras

simple holonomic modules over the second weyl algebra a2 abstract for simple generalized weyl algebras of gelfand kirillov dimension 4 a class including the second weyl algebra a 2 some simple factor algebras of the universal enveloping algebra of the lie algebra sl 2 sl 2 and of u q sl 2 u q sl 2 etc the simple holonomic modules are classified up to pairs of irreducible elements of certain noncommutative euclidean ring

whittaker modules for the twisted affine nappi witten lie algebra hˆ4 τ abstract the whittaker module m and its quotient whittaker module l for the twisted affine nappi witten lie algebra h 4 are studied for nonsingular type it is proved that if 0 then l is irreducible and any irreducible whittaker h 4 module of type with k acting as a non zero scalar is isomorphic to l furthermore for 0 all whittaker vectors of l 0 are completely determined for singular type the whittaker vectors of l with 0 are fully characterized

whittaker modules for heisenberg algebras and imaginary whittaker modules for affine lie algebras abstract we classify the irreducible whittaker modules for finite and infinite dimensional heisenberg algebras and for the lie algebra obtained by adjoining a degree derivation to an infinite dimensional heisenberg algebra we use these modules to construct a new class of modules for non twisted affine lie algebras which we call imaginary whittaker modules we show that the imaginary whittaker modules of non zero level are irreducible

whittaker modules for the affine lie algebra a_1 1 abstract we prove the irreducibility of the universal non degenerate whittaker modules for the affine lie algebra sl 2 of type a 1 1 with noncritical level these modules can become simple whittaker modules over sl 2 sl 2 c d with the same whittaker function and central charge we have to modulo a central character for sl 2 to obtain simple degenerate whittaker sl 2 modules with noncritical level in the case of critical level the universal whittaker module is reducible we prove that the quotient of universal whittaker sl 2 module by a submodule generated by a scalar action of central elements of the vertex algebra v 2 sl 2 is simple as sl 2 module we also explicitly describe the simple quotients of universal whittaker modules at the critical level for sl 2 quite surprisingly with the same whittaker function some simple degenerate sl 2 whittaker modules at the critical level have semisimple action of d and others have free action of d at last by using vertex algebraic techniques we present a wakimoto type construction of a family of simple generalized whittaker modules for sl 2 at the critical level this family includes all classical whittaker modules at critical level we also have wakimoto type realization for degenerate whittaker modules for sl 2 at noncritical level

a class of simple weight virasoro modules abstract for a simple module m over the positive part of the virasoro algebra actually for any simple module over some finite dimensional solvable lie algebras a r and any c a class of weight modules n m over the virasoro algebra is constructed these weight modules have infinite dimensional weight spaces if dim m 1 the necessary and sufficient conditions for n m to be simple are obtained we also determine the necessary and sufficient conditions for two such irreducible virasoro modules to be isomorphic many examples for such irreducible virasoro modules with different features are provided in particular the irreducible weight virasoro modules 1 2 1 2 are defined on the polynomial algebra c x c t t 1 for any 1 2 1 2 c with 1 or 2 nonzero by twisting the weight modules n m we also obtain nonweight simple virasoro modules n m for any nonconstant c t t 1

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

locally extended affine lie algebras abstract we propose a new simplified definition of extended affine lie algebras ealas for short and also discuss a general version of extended affine lie algebras called locally extended affine lie algebras local ealas for short we prove a conjecture by v kac for local ealas it turns out that the root system of a local eala becomes a locally finite version of an extended affine root system several examples of new ealas and local ealas are introduced and finally we classify local ealas of nullity 0 and show the connection to locally finite split simple lie algebras

whittaker modules for the schrodinger witt algebra in this paper whittaker modules for the schrodinger witt algebra sv are defined the whittaker vectors and the irreducibility of the whittaker modules are studied sv has a triangular decomposition according to its cartan subalgebra h sv sv h sv for any lie algebra homomorphism sv c we can define whittaker modules of type when is nonsingular the whittaker vectors the irreducibility and the classification of whittaker modules are completely determined when is singular by constructing some special whittaker vectors we find that the whittaker modules are all reducible moreover we get some more precise results for special

generalized mixture operators using weighting functions a comparative study with wa and owa abstract in the context of multiple attribute decision making we present an aggregation scheme based on generalized mixture operators using weighting functions and we compare it with two standard aggregation methods weighted averaging and ordered weighted averaging specifically we consider linear and quadratic weight generating functions that penalize bad attribute performances and reward good attribute performances an illustrative example borrowed from the literature is used to perform the operators comparison we believe that this comparative study will highlight the potential and flexibility of generalized mixture operators using weighting functions that depend on attribute performances

quasi whittaker modules for the schrodinger algebra abstract in this paper we construct a class of new modules for the schrodinger algebra s called quasi whittaker modules different from 30 the quasi whittaker module is not induced by the borel subalgebra of the schrodinger algebra related with the triangular decomposition but by its heisenberg subalgebra h we prove that a simple s module v is a quasi whittaker module if and only if v is a locally finite h module furthermore we classify simple quasi whittaker modules by central character of u s and their quasi whittaker functions finally we characterize arbitrary quasi whittaker modules

a classification of simple lie modules having a 1 dimensional weight space let l denote a simple lie algebra over the complex numbers in this paper we classify and construct all simple l modules which may be infinite dimensional but have at least one 1 dimensional weight space this completes the study begun earlier by the authors for the case of l a the approach presented here relies heavily on the results of suren fernando whose dissertation dealt with simple weight modules and their weight systems 0 introduction let l be a finite dimensional simple lie algebra over the complex field c having a cartan subalgebra h and denote by c l the centralizer of h in the universal enveloping algebra u of l if x h c is a weight function of a 1 dimensional weight space mx in a simple l module m then q c l c defined by q c v cv for v e mx and c e c l is an algebra homomorphism called a mass function of m clearly x restricted to h is equal to x conversely given any algebra homomorphism q c l c one can construct a unique simple l module which admits x as a mass function 4 10 in 4 the authors determined all algebra homomorphisms q c l c for the simple lie algebras l of type an and using these classified all pointed an modules where we call a module pointed if it is simple and has at least one 1 dimensional weight space in this paper we complete the classification of all pointed l modules for arbitrary simple lie algebras the collection of all pointed l modules clearly includes the highest weight l modules and is included in the collection of all harish chandra l modules relative to the cartan subalgebra h i e simple l modules having a weight space decomposition and finite dimensional weight spaces relative to h the latter inclusion is strict since there exist examples of harish chandra a2 modules in which every weight space is two dimensional in the special case of a1 modules every harish chandra a1 module is pointed our approach to this problem makes heavy use of the results from fernando s thesis 8 in particular from fernando s results we see that in place of determining all algebra homomorphisms q c l c it suffices to find only those algebra homomorphisms x which are associated with so called pointed torsion free l received by the editors may 23 1984 this paper was presented at the 1984 canadian mathematical society s summer seminar on lie algebras and related topics held at the university of windsor 1980 mathematics subject classification primary 17b10

whittaker modules for the twisted heisenberg virasoro algebra we define whittaker modules for the twisted heisenberg virasoro algebra and obtain several results from the classical setting including a classification of simple whittaker modules by central characters