Maximal injective and mixing masas in group factors

Paul Jolissaint

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arXiv · 1004.0128

Maximal injective and mixing masas in group factors

Paul Jolissaint

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Abstract

We present families of pairs of finite von Neumann algebras $A\subset M$ where $A$ is a maximal injective masa in the type $\mathrm{II}_1$ factor $M$ with separable predual. Our results make use of the strong mixing and the asymptotic orthogonality properties of $A$ in $M$ and are borrowed from ideas of S. Popa who proved that if $G$ is a non abelian free group and if $a$ is one of its generators, then the von Neumann algebra generated by $a$ is maximal injective in the factor $L(G)$. Our results apply to pairs $H<G$ where $H$ is an infinite abelian subgroup of a suitable amalgamated product group $G$.

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BibTeX RIS

Paul Jolissaint. 2010-04-01. Maximal injective and mixing masas in group factors. https://arxiv.org/abs/1004.0128

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