A class of ${\rm II_1}$ factors with an exotic abelian maximal amenable subalgebra

Details A class of ${\rm II_1}$ factors with an exotic abelian maximal amenable subalgebra A class of ${\rm II_1}$ factors with an exotic abelian maximal amenable subalgebra

2012-03-30

arxiv.org/abs/1203.6743v1

Mathematics

Operator Algebras

16 pages

Scientific paper

We show that for every mixing orthogonal representation $\pi : \Z \to \mathcal O(H_\R)$, the abelian subalgebra $\LL(\Z)$ is maximal amenable in the crossed product ${\rm II}_1$ factor $\Gamma(H_\R)\dpr \rtimes_\pi \Z$ associated with the free Bogoljubov action of the representation $\pi$. This provides uncountably many non-isomorphic $A$-$A$-bimodules which are disjoint from the coarse $A$-$A$-bimodule and of the form $\LL^2(M \ominus A)$ where $A \subset M$ is a maximal amenable masa in a ${\rm II_1}$ factor.

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