#### 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 ${\left(ℤ∕2ℤ\right)}^{\star k}$ 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
Primary: 46L10
Secondary: 46L65