Absolutely indecomposable representations of a twisted group algebra of a finite p-group over a field of characteristic p

Abstract

Let G be a non-cyclic finite p-group and K an infinite field of characteristic p. For every 2-cocycle λ ∈ Z 2 (G, K * ) such that the twisted group algebra K λ G is not uniserial, we find the integers m ≥ 1 for which K λ G has infinitely many absolutely indecomposable representations of dimension m. The main results of the paper imply a solution of the second Brauer-Thrall conjecture for the twisted group algebras K λ G, under some assumption on G and K.