Noncommutative Poisson boundaries and Furstenberg–Hamana boundaries of Drinfeld doubles

نویسندگان

چکیده

We clarify the relation between noncommutative Poisson boundaries and Furstenberg–Hamana of quantum groups. Specifically, given a compact group G, we show that in many cases where boundary dual discrete Gˆ has been computed, underlying topological either coincides with Drinfeld double D(G) G or is quotient it. This includes q-deformations Lie groups, free orthogonal unitary automorphism groups finite dimensional C⁎-algebras. In particular, D(Gq) for q-deformation connected semisimple Gq/T (for q≠1), agreement classical results Furstenberg Moore on GC. also construction respects monoidal equivalence and, fact, can be carried out entirely at level representation category G. leads to notion rigid C⁎-tensor category. Nous clarifions la entre frontières de non commutatives et des groupes quantiques. Plus précisément, étant donné un groupe quantique nous montrons que dans les nombreux cas où frontière du discret été calculé, topologique sous-jacente coïncide soit avec est celle-ci. Cela inclut q-déformations compacts, quantiques libres orthogonaux unitaires, d'automorphismes C⁎-algèbres dimension finie. En particulier, pour q-déformation d'un semi-simple connexe (pour en accord résultats classiques sur aussi respecte l'équivalence monoïdale et, fait, peut être réalisée entièrement au niveau catégorie représentation conduit à une d'une C⁎-catégorie tensorielle rigide.

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ژورنال

عنوان ژورنال: Journal de Mathématiques Pures et Appliquées

سال: 2022

ISSN: ['0021-7824', '1776-3371']

DOI: https://doi.org/10.1016/j.matpur.2021.12.006