Normal Forms for Representations of Representation-finite Algebras

Normal Forms for Representations of Representation-finite Algebras

Normal forms for algebras of connection

Recent years have seen a growing interest towards algebraic structures that are able to express formalisms di.erent from the standard, tree-like presentation of terms. Many of these approaches reveal a speci1c interest towards the application to the ‘distributed and concurrent systems’ 1eld, but an exhaustive comparison between them is sometimes di4cult, because their presentations can be quite...

Representations of Finite Lie Algebras

The notion of Frobenius morphisms for finite dimensional associative algebras is introduced in [2] and applied there to the study of representations of finite dimensional algebras over finite fields. In this paper, we develop a parallel theory for Lie algebras. Thus, a connection between representations over finite fields Fq and over their algebraic closures k = F̄q is established analogously. T...

Indecomposable Representations of Finite-Dimensional Algebras

Let 1c "be a field and A a finite-dimensional 7c-algebra (associative, with 1). AVe consider representations of A as rings of endomorpliisms of finitedimensional 7c-spaces, and thus JL-modules, and we ask for a classification of such representations. More generally, we may consider the following problem: given an abelian category # and simple ( = irreducible) objects F(l),..., B(n) in #, what a...

Finite Dimensional Representations of W -algebras

W -algebras of finite type are certain finitely generated associative algebras closely related to universal enveloping algebras of semisimple Lie algebras. In this paper we prove a conjecture of Premet that gives an almost complete classification of finite dimensional irreducible modules for W -algebras. Also we get some partial results towards a conjecture by Ginzburg on their finite dimension...