Deformation of operator algebras by Borel cocycles

2012/07/11 by Bhowmick, Jyotishman, Neshveyev, Sergey, Sangha, Amandip · 2 citations
#FOS: Mathematics #Operator Algebras (math.OA) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1207.2560

Abstract

Assume that we are given a coaction δof a locally compact group G on a C*-algebra A and a T-valued Borel 2-cocycle ωon G. Motivated by the approach of Kasprzak to Rieffel's deformation we define a deformation A_ωof A. Among other properties of A_ωwe show that A_ω⊗ K(L²(G)) is canonically isomorphic to A\rtimes_δ G\rtimes_δ,ωG. This, together with a slight extension of a result of Echterhoff et al., implies that for groups satisfying the Baum-Connes conjecture the K-theory of A_ωremains invariant under homotopies of omega.

Cited by

• Spectral-Geometric Deformations of Function Algebras on Manifolds
• Fischer's approach to deformation of coactions

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