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Solidity of Type III Bernoulli Crossed Products (2016)

Springer

In: Communications in Mathematical Physics

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Publication Date: 2016-07-21

Description: We generalize a theorem of Chifan and Ioana by proving that for any, possibly type III, amenable von Neumann algebra A 0 , any faithful normal state \({\varphi_0}\) and any discrete group \({\Gamma}\) , the associated Bernoulli crossed product von Neumann algebra \({M=(A_0,\varphi_0)^{\overline{\otimes} \Gamma} \rtimes \Gamma}\) is solid relatively to \({\mathcal{L}(\Gamma)}\) . In particular, if \({\mathcal{L}(\Gamma)}\) is solid then M is solid and if \({\Gamma}\) is non-amenable and \({A_0 \neq \mathbb{C}}\) then M is a full prime factor. This gives many new examples of solid or prime type III factors. Following Chifan and Ioana, we also obtain the first examples of solid non-amenable type III equivalence relations.

Print ISSN: 0010-3616

Electronic ISSN: 1432-0916

Topics: Mathematics , Physics

Published by Springer

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