Deformation of algebras associated with group cocycles

Abstract

We study deformation of algebras with coaction symmetry of reduced algebra of discrete groups, where the deformation parameter is given continuous family of group $2$-cocycles. When the group satisfies the Baum-Connes conjecture with coefficients, we obtain isomorphism of K-groups of the deformed algebras. This extends both the $\theta$-deformation of Rieffel on ${\mathbb{T}}^n$-actions, and a recent result of Echterhoff, Lück, Phillips, and Walters on the K-groups on the twisted group algebras.

v3: minor changes, to appear in JNCG; v2: 18 pages; v1: 15 pages

References in corpus (4)

• Quantized algebras of functions on homogeneous spaces with Poisson stabilizers
• The structure of crossed products of irrational rotation algebras by finite subgroups of SL_2 (Z)
• Connes-Landi Deformation of Spectral Triples
• K-homology class of the Dirac operator on a compact quantum group

Cited by in corpus (2)

• Deformation of C*-algebras by cocycles on locally compact quantum groups
• Compact Lie group actions with continuous Rokhlin property