A note on rigidity for crossed product von Neumann algebras

2006/06/27 by Tomohiro Hayashi, Hayashi, Tomohiro
Mathematics · #46L #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Holomorphic and Operator Theory #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.math/0606664

openalex publication_date 2006/06/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, we will point out, as a corollary of Popa's rigidity theory, that the crossed product von Neumann algebras for Bernoulli shifts cannot have relative property T. This is an operator algebra analogue of the theorem shown by Neuhauser and Cherix-Martin-Valette for discrete groups. Our proof is different from that for groups.

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