On group algebras of central group extensions

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...

Central Idempotents in Group Algebras

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∗).

On Central Extensions of Preprojective Algebras

μiei), where μ = (μi) is a regular weight (for the root system attached to Q), and ei are the vertex idempotents in P . 1 It is shown in [ER] that the algebra A has nicer properties than the ordinary Gelfand-Ponomarev preprojective algebra A0 = A/(z) of Q; in particular, the deformed version A(λ) of A = A(0) is flat, while this is not the case for A0. The paper [ER] also shows that A is a Frobe...