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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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A class of $\textrm {II_1}$ factors with an exotic abelian maximal amenable subalgebra
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by Cyril Houdayer PDF
Trans. Amer. Math. Soc. 366 (2014), 3693-3707 Request permission


We show that for every mixing orthogonal representation $\pi : \mathbf {Z} \to \mathcal O(H_{\mathbf {R}})$, the abelian subalgebra $\mathrm {L}(\mathbf {Z})$ is maximal amenable in the crossed product $\mathrm {II}_1$ factor $\Gamma (H_{\mathbf {R}})'' \rtimes _\pi \mathbf {Z}$ 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 $\mathrm {L}^2(M \ominus A)$ where $A \subset M$ is a maximal amenable masa in a $\mathrm {II}_1$ factor.
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Additional Information
  • Cyril Houdayer
  • Affiliation: Unité de Mathématiques Pures et Appliquées, École Normale Supérieure de Lyon, CNRS-UMR 5669, 69364 Lyon Cedex 7, France
  • Email:
  • Received by editor(s): April 30, 2012
  • Received by editor(s) in revised form: September 21, 2012
  • Published electronically: March 20, 2014
  • Additional Notes: The author’s research was partially supported by ANR grants AGORA NT09-461407 and NEUMANN
  • © Copyright 2014 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 366 (2014), 3693-3707
  • MSC (2010): Primary 46L10, 46L54, 46L55, 22D25
  • DOI:
  • MathSciNet review: 3192613