Examples of mixing subalgebras of von Neumann algebras and their normalizers

zbMATH Open1266.46046arXiv1103.5356MaRDI QIDQ690846

Paul Jolissaint

Publication date: 29 November 2012

Published in: Bulletin of the Belgian Mathematical Society - Simon Stevin (Search for Journal in Brave)

Abstract: We discuss different mixing properties for triples of finite von Neumann algebras $BsubsetNsubsetM$, and we introduce families of triples of groups $H<K<G$ whose associated von Neumann algebras $L(H)subsetL(K)subsetL(G)$ satisfy $$. It turns out that the latter equality is implied by two conditions: the equality $mathcal{N}_G(H)=K$ and the above mentioned mixing properties. Our families of examples also allow us to exhibit examples of pairs $H<G$ such that $$.

Full work available at URL: https://arxiv.org/abs/1103.5356

zbMATH Keywords

discrete groupsfinite von Neumann algebrasrelative weak asymptotic homomorphism propertyrelative weak mixing subalgebras

Mathematics Subject Classification ID

General theory of von Neumann algebras (46L10) Noncommutative dynamical systems (46L55) (C^*)-algebras and (W^*)-algebras in relation to group representations (22D25) Dynamical systems and the theory of (C^*)-algebras (37A55)

Related Items (2)

Mixing subalgebras of finite von Neumann algebras ⋮ On invariant von Neumann subalgebras rigidity property

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