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september 2012 Examples of mixing subalgebras of von Neumann algebras and their normalizers
Paul Jolissaint
Bull. Belg. Math. Soc. Simon Stevin 19(3): 399-413 (september 2012). DOI: 10.36045/bbms/1347642373


We discuss different mixing properties for triples of finite von Neumann algebras $B\subset N\subset M$, and we introduce families of triples of groups $H<K<G$ whose associated von Neumann algebras $L(H)\subset L(K)\subset L(G)$ satisfy $\mathcal{N}_{L(G)}(L(H))''=L(K)$. 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 $L(\mathcal{N}_G(H))\not=\mathcal{N}_{L(G)}(L(H))''$.


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Paul Jolissaint. "Examples of mixing subalgebras of von Neumann algebras and their normalizers." Bull. Belg. Math. Soc. Simon Stevin 19 (3) 399 - 413, september 2012.


Published: september 2012
First available in Project Euclid: 14 September 2012

zbMATH: 1266.46046
MathSciNet: MR3027351
Digital Object Identifier: 10.36045/bbms/1347642373

Primary: 46L10
Secondary: 22D25

Keywords: discrete groups , Finite von Neumann algebras , relative weak asymptotic homomorphism property , relative weak mixing subalgebras

Rights: Copyright © 2012 The Belgian Mathematical Society


Vol.19 • No. 3 • september 2012
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