POISSON BOUNDARIES OVER LOCALLY COMPACT QUANTUM GROUPS

DOI10.1142/S0129167X13500237zbMath1327.46072arXiv1111.5828OpenAlexW2005530160MaRDI QIDQ4923307

Zhong-Jin Ruan, Mehrdad Kalantar, Matthias Neufang

Publication date: 6 June 2013

Published in: International Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1111.5828

zbMATH Keywords

Poisson boundaryamenabilityharmonic functionslocally compact quantum groupsChoquet-Deny theorem

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Operator spaces and completely bounded maps (46L07) Noncommutative probability and statistics (46L53) Other ``noncommutative mathematics based on (C^*)-algebra theory (46L89) Boundary theory for Markov processes (60J50) Quantizations, deformations for selfadjoint operator algebras (46L65)

Related Items (6)

Harmonic operators of ergodic quantum group actions ⋮ Ideals of the Fourier algebra, supports and harmonic operators ⋮ Convolution semigroups on locally compact quantum groups and noncommutative Dirichlet forms ⋮ Idempotent states on Sekine quantum groups ⋮ On harmonic non-commutative $L^p$-operators on locally compact quantum groups ⋮ Fixed points and limits of convolution powers of contractive quantum measures

Cites Work

• Unnamed Item
• Non-commutative Poisson boundaries and compact quantum group actions
• A new characterisation of idempotent states on finite and compact quantum groups
• Poisson boundary of the dual of \(\text{SU}_q(n)\).
• On locally compact quantum groups whose algebras are factors
• Quantum spheres
• Random walks on discrete groups: Boundary and entropy
• Twisted \(\text{SU}(2)\) group. An example of a non-commutative differential calculus
• Ergodic and mixing random walks on locally compact groups
• A characterization of right coideals of quotient type and its application to classification of Poisson boundaries
• The boundary of universal discrete quantum groups, exactness, and factoriality
• Completely bounded multipliers over locally compact quantum groups
• IDEMPOTENT STATES ON LOCALLY COMPACT QUANTUM GROUPS
• Poisson boundary of the discrete quantum group
• Amenability and Co-Amenability for Locally Compact Quantum Groups
• Strictly Outer Actions of Groups and Quantum Groups
• LOCALLY COMPACT QUANTUM GROUPS IN THE UNIVERSAL SETTING
• Multipliers on a new class of Banach algebras, locally compact quantum groups, and topological centres
• Uniform continuity over locally compact quantum groups
• On ergodic properties of convolution operators associated with compact quantum groups
• IDENTIFICATION OF THE POISSON AND MARTIN BOUNDARIES OF ORTHOGONAL DISCRETE QUANTUM GROUPS

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