Group Algebras Satisfying a Certain Lie Identity

It is shown that (1) every almost self-injective group algebra is self-injective and (2) if the group algebra KG is continuous, then G is a locally finite group. Furthermore, it follows that the following assertions are equivalent: a CS group algebra KG is continuous; KG is principally self-injective; the group G is locally finite.

We classify, in terms of the structure of the finite group G, all group algebras KG for which all right ideals are right annihilators of principal left ideals. This means in the language of coding theory that we classify code-checkable group algebras KG which have been considered so far only for abelian groups G. Optimality of checkable codes and asymptotic results are discussed.

A deformation-theoretic version of Maschke's theorem for modular group algebras: The commutative case

Let K be any field of characteristic zero. We show that there are at least four ideals in the group algebra KG of every simple locally finite group G of 1-type, thus providing the final step in solving an old question of I. Kaplansky's for locally finite groups. We also determine the ideal lattice in KG for those 1-type groups G which are a direct limit of finite direct products of alternating groups.

On modules with cyclic vertices in the Auslander-Reiten quiver

A cluster tilting module for a representation-infinite block of a group algebra

Lie properties of symmetric elements in group rings

We define classes of automorphically rigid modular group algebras KG over a finite field K and a finite group G.

Using representation theoretical methods we investigate self-dual group codes and their extensions in characteristic 2. We prove that the existence of a self-dual extended group code heavily depends on a particular structure of the group algebra KG which can be checked by an easy-to-handle criteria in elementary number theory. Surprisingly, in the binary case such a code is doubly even if the converse of Gleason's theorem holds true, i.e., the length of the code is divisible by 8. Furthermore, we give a short representation theoretical proof of an earlier result of Sloane and Thompson which states that a binary self-dual group code is never doubly even if the Sylow 2-subgroups of G are cyclic. It turns out that exactly in the case of a cyclic or Klein four group as Sylow 2-subgroup doubly even group codes do not exist.