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arXiv · 1207.2560

Deformation of operator algebras by Borel cocycles

Jyotishman Bhowmick·Sergey Neshveyev·Amandip Sangha
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Abstract

Assume that we are given a coaction \delta of a locally compact group G on a C*-algebra A and a T-valued Borel 2-cocycle \omega on G. Motivated by the approach of Kasprzak to Rieffel's deformation we define a deformation A_\omega of A. Among other properties of A_\omega we show that A_\omega\otimes K(L^2(G)) is canonically isomorphic to A\rtimes_\delta\hat G\rtimes_{\hat\delta,\omega}G. 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_\omega remains invariant under homotopies of omega.

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Jyotishman Bhowmick, Sergey Neshveyev, Amandip Sangha. 2012-07-11. Deformation of operator algebras by Borel cocycles. https://doi.org/10.1016/j.jfa.2013.05.021

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