A strong Connes spectrum for finite group actions of simple rings
This is the second in a series of papers which develop algebraic analogs of the Connes spectrum. The first, by \textit{S. Montgomery} and the reviewer [J. Algebra 115, 92-124 (1988; Zbl 0639.16002)] studied the smash product \(A\#k[G]^*\) where \(k[G]^*\) is the dual of the group algebra \(k[G]\) of the finite group \(G\). This paper considers the skew group ring \(AG=A\#k[G]^*\) and obtains necessary and sufficient conditions for the ring to be simple in terms of the irreducible representations of \(G\). More recently, these results have been extended to the general Hopf algebra smash product situation in various papers by J. Osterburg, D. Quinn and the reviewer. In particular, there is now a general definition for the Connes spectrum of a finite dimensional Hopf algebra \(H\) acting on the \(H\)-module algebra \(A\) and there are necessary and sufficient conditions for the smash product \(A\# H\) to be prime or simple.
scientific article; zbMATH DE number 23608
scientific article