Poisson boundary of the discrete quantum group

DOI10.1112/S0010437X1000477XzbMath1204.46035arXiv0812.0804OpenAlexW3121613534MaRDI QIDQ3577321

Nikolas Vander Vennet, Stefaan Vaes

Publication date: 22 July 2010

Published in: Compositio Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0812.0804

zbMATH Keywords

Martin boundaryPoisson boundaryrandom walkboundary actioncompact quantum groupfree quantum groupdiscrete quantum groupsolid II\(_1\) factor

Mathematics Subject Classification ID

Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Free probability and free operator algebras (46L54) Noncommutative probability and statistics (46L53) Boundary theory for Markov processes (60J50) Quantizations, deformations for selfadjoint operator algebras (46L65)

Related Items (16)

Noncommutative Furstenberg boundary ⋮ Unique prime factorization and bicentralizer problem for a class of type III factors ⋮ Realization of quantum group Poisson boundaries as crossed products ⋮ On the \({\ell}^2\)-Betti numbers of universal quantum groups ⋮ Noncommutative Poisson boundaries and Furstenberg-Hamana boundaries of Drinfeld doubles ⋮ Examples of factors which have no Cartan subalgebras ⋮ Poisson boundary on full Fock space ⋮ Paths in quantum Cayley trees and \(L^{2}\)-cohomology ⋮ Probabilistic boundaries of finite extensions of quantum groups ⋮ Cartan subalgebras of tensor products of free quantum group factors with arbitrary factors ⋮ Martin boundaries of the duals of free unitary quantum groups ⋮ Product type actions of \(G_q\) ⋮ Some prime factorization results for free quantum group factors ⋮ POISSON BOUNDARIES OVER LOCALLY COMPACT QUANTUM GROUPS ⋮ On harmonic non-commutative $L^p$-operators on locally compact quantum groups ⋮ Ergodic properties and harmonic functionals on locally compact quantum groups

Cites Work

• Actions of monoidally equivalent compact quantum groups and applications to probabilistic boundaries

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