Deformation of algebras associated with group cocycles

2011/07/13 by Makoto Yamashita, Yamashita, Makoto
Mathematics · #46L80 (Primary) 46L65 #58B34 (Secondary) #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1107.2512

openalex publication_date 2011/07/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 θ-deformation of Rieffel on \mathbb Tⁿ-actions, and a recent result of Echterhoff, Lück, Phillips, and Walters on the K-groups on the twisted group algebras.

Citations

• The structure of crossed products of irrational rotation algebras by finite subgroups of SL₂ (Z)
• Equivariant Poincaré duality for quantum group actions

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