Simple Modules for Kumjian-Pask Algebras

O Algebras with Three Simple Modules

0. Introduction. In D], Dyer has introduced the concept of O algebra, this is a basic quasi-hereditary Koszul algebra with an anti-involution, such that its quadratic dual is also quasi-hereditary. Typical examples of such algebras are ones associated with blocks of category O of Bernstein-Gelfand-Gelfand BGG], see also Beilinson-Ginsburg-Soergel BGS]. The present paper grew out of a desire to ...

Simple modules of Ariki{Koike algebras

Centers and Simple Modules for Iwahori-hecke Algebras

The work of Dipper and James on Iwahori-Hecke algebras associated with the finite Weyl groups of type An has shown that these algebras behave in many ways like group algebras of finite groups. Moreover, there are “generic” features in the modular representation theory of these algebras which, at present, can only be verified in examples by explicit computations. This paper arose from an attempt...

Simple modules for the restricted Cartan type Lie algebras

The simple modules with homogeneous characters are considered, their dimension formulas are determined.

Factorization of Simple Modules for Certain Pointed Hopf Algebras

We study the representations of two types of pointed Hopf algebras: restricted two-parameter quantum groups, and the Drinfel’d doubles of rank one pointed Hopf algebras of nilpotent type. We study, in particular, under what conditions a simple module can be factored as the tensor product of a one dimensional module with a module that is naturally a module for the quotient by central group-like ...