Simple reflexive modules over finite-dimensional algebras

Locally Finite Simple Weight Modules over Twisted Generalized Weyl Algebras

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 to...

Modules with Few Types over Some Finite-Dimensional Algebras

Computing Homomorphism Spaces between Modules over Finite Dimensional Algebras

In this paper, we study the fundamental algorithmic problem of determining the homomorphisms from an Amodule M to an A-module N over an algebra A. We shall outline an algorithm for the case that A is a finite dimensional algebra over a finite field F and both modules M and N are finitely generated as A-modules. More specifically, the input to our algorithm consists of the following data: The mo...

Finite-dimensional Simple Poisson Modules

We prove a result that can be applied to determine the finitedimensional simple Poisson modules over a Poisson algebra and apply it to numerous examples. In the discussion of the examples, the emphasis is on the correspondence with the finite-dimensional simple modules over deformations and on the behaviour of finite-dimensional simple Poisson modules on the passage from a Poisson algebra to th...

Finite dimensional graded simple algebras

Let R be a finite-dimensional algebra over an algebraically closed field F graded by an arbitrary group G. We prove that R is a graded division algebra if and only if it is isomorphic to a twisted group algebra of some finite subgroup of G. If the characteristic of F is zero or char F does not divide the order of any finite subgroup of G then we prove that R is graded simple if and only if it i...