Algebraic analogs of the Connes spectrum (Q1100252)

Let \(G\) be a finite group and let \(A\) be a \(G\)-graded ring with 1. From the theory of Hopf algebras the smash product \(A{\#}G^*\), an extension ring of \(A\) is introduced. The authors introduce the Connes and the strong Connes subgroup of \(G\) and relate them to the ideal structure of \(A{\#}G^*\). From this criteria for \(A{\#}G^*\) to be prime or simple are derived. Now let \(A\) be a \(K\)-algebra and \(G\) an Abelian group acting as \(K\)-algebra automorphisms on \(A\). If \(K\) contains certain roots of unity then the skew group ring \(AG\) has a smash product structure \(A{\#}\widehat G^*\) where \(\widehat G=\Hom(G,K^.)\) is the dual group of \(G\). If \(A\) is a prime ring, the authors determine the Connes subgroup of \(\widehat G\) in terms of the action of \(G\) on \(A\).