Strongly singular MASA's and mixing actions in finite von Neumann algebras

Details Strongly singular MASA's and mixing actions in finite von Neumann algebras Strongly singular MASA's and mixing actions in finite von Neumann algebras

2006-02-08

arxiv.org/abs/math/0602158v3

Mathematics

Operator Algebras

Title updated, examples and references added. To appear in Ergod. Th. & Dynam. Syst

Scientific paper

Let $\Gamma$ be a countable group and let $\Gamma_0$ be an infinite abelian subgroup of $\Gamma$. We prove that if the pair $(\Gamma,\Gamma_0)$ satisfies some combinatorial condition called (SS), then the abelian subalgebra $A=L(\Gamma_0)$ is a singular MASA in $M=L(\Gamma)$ which satisfies a weakly mixing condition. If moreover it satisfies a stronger condition called (ST), then it provides a singular MASA with a strictly stronger mixing property. We describe families of examples of both types coming from free products, HNN extentions and semidirect products, and in particular we exhibit examples of singular MASA's that satisfy the weak mixing condition but not the strong mixing one.

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