On masas in $q$-deformed von Neumann algebras

Martijn Caspers, Adam Skalski and Mateusz Wasilewski

Vol. 302 (2019), No. 1, 1–21

DOI: 10.2140/pjm.2019.302.1

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 ${\left(\mathbb{Z}∕2\mathbb{Z}\right)}^{\star k}$ and shown to be a maximal abelian subalgebra which is singular and with Pukánszky invariant $\left\{\infty \right\}$. 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