Regularizations of twisted covariant systems and crossed products with continuous trace
Given a twisted covariant system \((G, A, \tau)\), it is not easy to determine the topology of the primitive ideal space. In order to improve this situation, the author defines a regularization of \((G, A, \tau)\) as a pair \((\Omega, R)\) of a locally compact space \(\Omega\) and a continuous \(G\)-equivariant map \(R\) from Prim \((A)\) into \(\Omega\). He shows that regularization can be a useful tool for determining the structure of twisted crossed products. This is particularly the case when \(\Omega\) is a locally \(\sigma\)-trivial \(G\)-space: then each element in \(C^*(G, A, \tau)^ \wedge\) has a neighbourhood which can be described in terms of an appropriate subgroup algebra. In particular induced systems are exactly those which have \(\sigma\)-trivial regularizations where \(R\) is open and surjective. On the other hand, regularization allows to investigate whether certain crossed products have continuous trace.
scientific article; zbMATH DE number 515259