Bulletin of the Belgian Mathematical Society - Simon Stevin

Examples of mixing subalgebras of von Neumann algebras and their normalizers

Paul Jolissaint

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Abstract

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 $L(\mathcal{N}_G(H))\not=\mathcal{N}_{L(G)}(L(H))''$.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 19, Number 3 (2012), 399-413.

Dates
First available in Project Euclid: 14 September 2012

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1347642373

Digital Object Identifier
doi:10.36045/bbms/1347642373

Mathematical Reviews number (MathSciNet)
MR3027351

Zentralblatt MATH identifier
1266.46046

Subjects
Primary: 46L10: General theory of von Neumann algebras
Secondary: 22D25: $C^*$-algebras and $W^*$-algebras in relation to group representations [See also 46Lxx]

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

Citation

Jolissaint, Paul. Examples of mixing subalgebras of von Neumann algebras and their normalizers. Bull. Belg. Math. Soc. Simon Stevin 19 (2012), no. 3, 399--413. doi:10.36045/bbms/1347642373. https://projecteuclid.org/euclid.bbms/1347642373


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