2014/05/31 by Sergey Neshveyev, Makoto Yamashita · 1 citation
Mathematics · #Advanced Operator Algebra Research #Algebra over a field #Algebraic structures and combinatorial models #Closed monoidal category #Discrete mathematics #Exact solutions in general relativity #Functor #Homotopy and Cohomology in Algebraic Topology #Isomorphism (crystallography) #Mathematical analysis #Mathematics #Pure mathematics #Simple (philosophy) #Symmetric monoidal category #Tensor (intrinsic definition) #Tensor field #Tensor product #Unit (ring theory) #Unitary state #math.CT #math.OA #math.PR #math.QA #msc:18D10 #msc:46L50 #msc:60J50
paper · pdf · doi:10.24033/asens.2335
published as Ann. Sci. Éc. Norm. Supér. (4) 50 (2017), no. 4, 927-972 · v2: 37 pages, minor changes, to appear in Ann. Sci. Ecole Norm. Sup.; v1: 37 pages
openalex publication_date 2017/01/01 · arxiv created 2017/06/29 · arxiv updated 2021/06/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Abstract. Given a rigid C∗-tensor category C with simple unit and a probability measure µ on the set of isomorphism classes of its simple objects, we define the Poisson boundary of (C, µ). This is a new C∗-tensor category P, generally with nonsimple unit, together with a unitary tensor functor Π: C → P. Our main result is that if P has simple unit (which is a condition on some classical random walk), then Π is a universal unitary tensor functor defining the amenable dimension function on C. Corollaries of this theorem unify various results in the literature on amenability of C∗-tensor categories, quantum groups, and subfactors.