Examples of mixing subalgebras of von Neumann algebras and their normalizers

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 $L({\mathcal{N}}_G(H))\ne {\mathcal{N}}_{L(G)}(L(H))"$.

arXiv commentTo appear in the Bulletin of the Belgian Math. Soc. S. Stevin; Definition 2.1 has been modified under suggestion of the referee

References in corpus (1)

• Strong Singularity of Singular Masas in II_1 Factors