On masas in q-deformed von neumann algebras

Martijn Caspers; Adam Skalski; Mateusz Wasilewski

doi:10.2140/pjm.2019.302.1

On masas in q-deformed von neumann algebras

Martijn Caspers, Adam Skalski, Mateusz Wasilewski

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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 (Z=2Z)^k and shown to be a maximal abelian subalgebra which is singular and with Pukanszky invariant [∞]. Further all nonequal generator masas in the q-deformed Gaussian von Neumann algebras are shown to be mutually nonintertwinable.

Original language	English
Pages (from-to)	1-21
Number of pages	21
Journal	Pacific Journal of Mathematics
Volume	302
Issue number	1
DOIs	https://doi.org/10.2140/pjm.2019.302.1
Publication status	Published - 2019

Keywords

Hecke von neumann algebra
Maximal abelian subalgebras
Q-Gaussian algebras
Singular masas

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AU - Skalski, Adam

AU - Wasilewski, Mateusz

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AB - 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 (Z=2Z)k and shown to be a maximal abelian subalgebra which is singular and with Pukanszky invariant [∞]. Further all nonequal generator masas in the q-deformed Gaussian von Neumann algebras are shown to be mutually nonintertwinable.

KW - Hecke von neumann algebra

KW - Maximal abelian subalgebras

KW - Q-Gaussian algebras

KW - Singular masas

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SP - 1

EP - 21

JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

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ER -

On masas in q-deformed von neumann algebras

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Keywords

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