Central twisted group algebras

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].

Central Idempotents in Group Algebras

Twisted Lie group C-algebras as strict quantizations

A nonzero 2-cocycle Γ ∈ Z(g,R) on the Lie algebra g of a compact Lie group G defines a twisted version of the Lie-Poisson structure on the dual Lie algebra g∗, leading to a Poisson algebra C∞(g∗(Γ)). Similarly, a multiplier c ∈ Z (G, U(1)) on G which is smooth near the identity defines a twist in the convolution product on G, encoded by the twisted group C∗algebra C∗(G, c). Further to some supe...

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].