A new approach to deformation of $C^*$-algebras via coactions
Volume 281 / 2025
Studia Mathematica 281 (2025), 117-169
MSC: Primary 46L55; Secondary 22D35
DOI: 10.4064/sm240208-25-9
Published online: 10 February 2025
Abstract
We revisit the procedure of deformation of $C^*$-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 (2013).
Our approach yields all expected results, like a good behaviour of deformations under nuclearity, continuity of fields of $C^*$-algebras and $K$-theory invariance under mild conditions.
