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Strongly singular MASAs and mixing actions in finite von Neumann algebras

Published online by Cambridge University Press:  15 September 2008

PAUL JOLISSAINT  and
YVES STALDER
PAUL JOLISSAINT
Affiliation:
Université de Neuchâtel, Institut de Mathémathiques, Emile-Argand 11, Case postale 158, CH-2009 Neuchâtel, Switzerland (email: [email protected])
YVES STALDER
Affiliation:
Laboratoire de Mathématiques, Université Blaise Pascal, Campus universitaire des Cézeaux, 63177 Aubière Cedex, France (email: [email protected])
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Abstract

Let Γ be a countable group and let Γ0 be an infinite abelian subgroup of Γ. We prove that if the pair (Γ,Γ0) satisfies some combinatorial condition called (SS), then the abelian subalgebra A=L(Γ0) is a singular MASA in M=L(Γ) 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, Higman–Neumann–Neumann extensions and semidirect products, and in particular we exhibit examples of singular MASAs that satisfy the weak mixing condition but not the strong mixing one.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 28 , Issue 6 , December 2008 , pp. 1861 - 1878
Copyright
Copyright © 2008 Cambridge University Press

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