Maximal amenable MASAs of the free group factor of two generators arising from the free products of hyperfinite factors

Koichi Shimada

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arXiv · 1609.09617

Maximal amenable MASAs of the free group factor of two generators arising from the free products of hyperfinite factors

Koichi Shimada

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Abstract

In this paper, we give examples of maximal amenable subalgebras of the free group factor of two generators. More precisely, we consider two copies of the hyperfinite factor $R_i$ of type $\mathrm{II}_1$. From each $R_i$, we take a Haar unitary $u_i$ which generates a Cartan subalgebra of it. We show that the von Neumann subalgebra generated by the self-adjoint operator $u_1+u_1^{-1}+u_2+u_2^{-1}$ is maximal amenable in the free product. This provides infinitely many non-unitary conjugate maximal amenable MASAs.

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Koichi Shimada. 2016-09-30. Maximal amenable MASAs of the free group factor of two generators arising from the free products of hyperfinite factors. https://arxiv.org/abs/1609.09617

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