Group Algebras With Central Radicals

Central Idempotents in Group Algebras

Group Actions on Central Simple Algebras

Let G be a group, F a field, and A a finite-dimensional central simple algebra over F on which G acts by F -algebra automorphisms. We study the ideals and subalgebras of A which are preserved by the group action. Let V be the unique simple module of A. We show that V is a projective representation of G and A = EndD(V ) makes V into a projective representation. We then prove that there is a natu...

Primitive Central Idempotents of Nilpotent Group Algebras

We exhibit the primitive central idempotents of a semisimple group algebra of a finite nilpotent group over an arbitrary field (without using group characters), examining the abelian case separately. Our result extends and improves the main result in [1].

AMENABILITY OF VECTOR VALUED GROUP ALGEBRAS

The purpose of this article is to develop the notions of amenabilityfor vector valued group algebras. We prove that L1(G, A) is approximatelyweakly amenable where A is a unital separable Banach algebra. We givenecessary and sufficient conditions for the existence of a left invariant meanon L∞(G, A∗), LUC(G, A∗), WAP(G, A∗) and C0(G, A∗).

Group Algebras and Enveloping Algebras with Nonmatrix and Semigroup Identities

Let K be a field of characteristic p > 0. Denote by ω(R) the augmentation ideal of either a group algebra R = K[G] or a restricted enveloping algebra R = u(L) over K. We first characterize those R for which ω(R) satisfies a polynomial identity not satisfied by the algebra of all 2× 2 matrices over K. Then, we examine those R for which ω(R) satisfies a semigroup identity (that is, a polynomial i...