Vol. 302, No. 1, 2019

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On masas in $q$-deformed von Neumann algebras

Martijn Caspers, Adam Skalski and Mateusz Wasilewski

Vol. 302 (2019), No. 1, 1–21
Abstract

We study certain q-deformed analogues of the maximal abelian subalgebras of the group von Neumann algebras of free groups. The radial subalgebra is defined for Hecke deformed von Neumann algebras of the Coxeter group (2)k and shown to be a maximal abelian subalgebra which is singular and with Pukánszky invariant {}. Further all nonequal generator masas in the q-deformed Gaussian von Neumann algebras are shown to be mutually nonintertwinable.

Keywords
maximal abelian subalgebras, singular masas, Hecke von Neumann algebra, q-Gaussian algebras
Mathematical Subject Classification 2010
Primary: 46L10
Secondary: 46L65
Milestones
Received: 10 April 2017
Revised: 17 February 2019
Accepted: 18 February 2019
Published: 5 November 2019
Authors
Martijn Caspers
Mathematisch Instituut
Universiteit Utrecht
Utrecht
The Netherlands
Delft University of Technology
Delft
Netherlands
Adam Skalski
Institute of Mathematics
Polish Academy of Sciences
Warszaw
Poland
Mateusz Wasilewski
Institute of Mathematics
Polish Academy of Sciences
Warsaw
Poland
Department of Mathematics
Katholieke Universiteit Leuven
Leuven
Belgium