## Bulletin of the Belgian Mathematical Society - Simon Stevin

### Examples of mixing subalgebras of von Neumann algebras and their normalizers

Paul Jolissaint

#### 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

https://projecteuclid.org/euclid.bbms/1347642373

Digital Object Identifier
doi:10.36045/bbms/1347642373

Mathematical Reviews number (MathSciNet)
MR3027351

Zentralblatt MATH identifier
1266.46046

#### 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