Summary: JOURNAL OF
EISEkER Journal of Pure and Applied Algebra 94 (1994) l-15
Semisimple algebras, Galois actions and group cohomology
Eli Aljadeff *sa, Derek J.S. Robinson**gb
aDepartment of Mathematics, Technion - Israel Institute of Technology, 32000 Haifa, Israel
bDepartment of Mathematics, University of Illinois, Urbana-Champaign, 1409 West Green Street,
Urbana, IL 61801. USA
Communicated by K.W. Gruenberg; received 6 November 1992
Let K be any field of characteristic p > 0 and let G be a finite group acting on K via a map T.
The skew group algebra K,G may be non-semisimple (precisely when pIIH/, H = Kerr).
We provide necessary conditions for the existence of a class c(EH'(G, K*) which "twists" the
skew group algebra K, G into a semisimple crossed product Kr G. Further, we give a thorough
analysis of the converse problem namely whether these conditions are also sufficient 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 is a p-group.
If G is a finite group and K is a field, the classical theorem of Maschke asserts that