Simple Twisted Group Algebras of Dimensionp4and their Semi-Centers

Semi-simple Lie Algebras and Their Representations

This paper presents an overview of the representations of Lie algebras, particularly semi-simple Lie algebras, with a view towards theoretical physics. We proceed from the relationship between Lie algebras and Lie groups to more abstract characterizations of Lie groups, give basic definitions of different properties that may characterize Lie groups, and then prove results about root systems, pr...

Semi-Simple Lie Algebras and Their Representations

Twisted automorphisms of group algebras

We continue the study of twisted automorphisms of Hopf algebras started in [4]. In this paper we concentrate on the group algebra case. We describe the group of twisted automorphisms of the group algebra of a group of order coprime to 6. The description turns out to be very similar to the one for the universal enveloping algebra given in [4].

Semi-Simple Commutative Algebras with Positive Bases

Algebras that serve as models for concurrent studying of certain aspects of both the algebra of ordinary characters and the center of the group algebra have been considered by various authors. In this article we o¤er another such model. The main di¤erences between our model and the known ones are: 1. Our model includes Brauer characters and principal indecomposable characters as special cases. ...

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...