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Poisson boundary of the discrete quantum group

Part of: Selfadjoint operator algebras Groups and algebras in quantum theory Markov processes

Published online by Cambridge University Press:  08 June 2010

Stefaan Vaes  and
Nikolas Vander Vennet
Stefaan Vaes
Affiliation:
Department of Mathematics, K.U. Leuven, Celestijnenlaan 200B, B–3001 Leuven, Belgium (email: stefaan.vaes@wis.kuleuven.be)
Nikolas Vander Vennet
Affiliation:
Department of Mathematics, K.U. Leuven, Celestijnenlaan 200B, B–3001 Leuven, Belgium (email: nvandervennet@gmail.com)
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Abstract

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We identify the Poisson boundary of the dual of the universal compact quantum group Au(F) with a measurable field of ITPFI (infinite tensor product of finite type I) factors.

Keywords

discrete quantum groupcompact quantum grouprandom walkPoisson boundaryMartin boundaryfree quantum groupsolid II1 factorboundary action

MSC classification

Secondary: 46L53: Noncommutative probability and statistics 46L54: Free probability and free operator algebras 60J50: Boundary theory 81R50: Quantum groups and related algebraic methods
Type
Research Article
Information
Compositio Mathematica , Volume 146 , Issue 4 , July 2010 , pp. 1073 - 1095
Copyright
Copyright © Foundation Compositio Mathematica 2010

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