A new approach to deformation of C*-algebras via coactions

Abstract

We revisit the procedure of deformation of $C^{\ast }$-algebras via coactions of locally compact groups and extend the methods to cover deformations for maximal, reduced, and exotic coactions for a given group $G$ and circle-valued Borel $2$-cocycles on $G$. In the special case of reduced (or normal) coactions our deformation method substantially differs from -- but turns out to be equivalent to -- the ones used by previous authors, specially those given by Bhowmick, Neshveyev, and Sangha in [7]. Our approach yields all expected results, like a good behaviour of deformations under nuclearity, continuity of fields of $C^{\ast }$-algebras and $K$-theory invariance under mild conditions.

38 pages, final version to appear in Studia Math