The Nonvanishing First Hochschild Cohomology of Twisted Finite Simple Group Algebras

Abstract

Let G be a finite simple group and k be an algebraically closed field of prime characteristic dividing the order of G. We show that for all 2-cocycles α ∈ Z²(G;k^×), the first Hochschild cohomology group of the twisted group algebra HH¹(k_αG) is nonzero.