Some Structure Theory for Crossed Products by Finite Groups

Abstract

Our main interest is in structural results for crossed products. We want simplicity, but we really want much more than that. We particularly want theorems showing that certain crossed products are in classes of C*-algebras known to be covered by the Elliott classification program, so that the crossed product can be identified up to isomorphism by computing its K-theory and other invariants. In many cases, one settles for related weaker structural results, such as stable rank one, real rank zero, order on traces determined by projections, strict comparison of positive elements, or Z-stability. Some results with conclusions of this sort are stated in these notes, but mostly without proof.