SEMISIMPLE ALGEBRAS, GALOIS ACTIONS AND GROUP COHOMOLOGY

Let K be any field of characteristic p > 0 and let G be a finite group acting on K via a map tau. The skew group algebra K(tau)G may be non- semisimple (precisely when p\\H\, H = Ker tau). We provide necessary c onditions for the existence of a class alpha is-an-element-of H-2(G, K ) which ''twists'' the skew group algebra K(tau)G into a semisimple c rossed product K(tau)(alpha)G. Further, we give a thorough analysis of the converse problem namely whether these conditions are also suffici ent for the existence of a ''semisimple 2-cocycle''. As a consequence we show this it is indeed so in many cases, in particular whenever G i s a p-group.