Semisimple algebras, Galois actions and group cohomology

Eli Aljadeff*, Derek J.S. Robinson

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

Let K be any field of characteristic p>0 and let G be a finite group acting on K via a map τ. The skew group algebra KτG may be non-semisimple (precisely when p∥H|, H = Kerτ). We provide necessary conditions for the existence of a class αε{lunate}H2(G, K*) which "twists" the skew group algebra K>τG into a semisimple crossed product KατG. 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.

Original languageEnglish
Pages (from-to)1-15
Number of pages15
JournalJournal of Pure and Applied Algebra
Volume94
Issue number1
DOIs
StatePublished - 3 Jun 1994
Externally publishedYes

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