Amenable discrete quantum groups

2006/10/01 by Reiji Tomatsu, Reiji TOMATSU · 4 citations
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Discrete group #Discrete mathematics #Group (periodic table) #Invariant (physics) #Mathematical physics #Mathematics #Physics #Pure mathematics #Quantum #Quantum mechanics

paper · doi:10.2969/jmsj/1179759531

crossref issued 2006/10/01 · crossref published 2006/10/01 · crossref published-print 2006/10/01 · openalex publication_date 2006/10/01 · crossref created 2007/11/20 · crossref deposited 2021/05/09 · openalex created_date 2025/10/10 · crossref indexed 2026/08/03 · openalex updated_date 2026/08/04

Abstract

Z.-J. Ruan has shown that several amenability conditions are all equivalent in the case of discrete Kac algebras. In this paper, we extend this work to the case of discrete quantum groups. That is, we show that a discrete quantum group, where we do not assume its unimodularity, has an invariant mean if and only if it is strongly Voiculescu amenable.

Citations

• Kac Algebras and Duality of Locally Compact Groups
• Notes on Compact Quantum Groups
• Locally compact quantum groups
• Classification of Injective Factors Cases II 1 , II ∞ , III λ , λ � 1

Cited by

• Amenability of locally compact quantum groups via the long-time behavior of convolution semigroups
• Poisson boundaries of monoidal categories
• Cuntz Semigroups of Compact-Type Hopf C*-Algebras
• Amenability of locally compact quantum groups and their unitary co-representations