2016/09/30 by Chi–Keung Ng, Chi-Keung Ng, Ami Viselter
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Compact group #Compact quantum group #Corollary #Group (periodic table) #Lie group #Locally compact group #Locally compact space #Mathematics #Physics #Pure mathematics #Quantum #Quantum mechanics #Unitary group #Unitary representation #Unitary state #math.FA #math.OA #msc:20G42 #msc:22D25 #msc:46L89
paper · pdf · doi:10.1112/blms.12047
published as Bull. Lond. Math. Soc. 49 (2017), no. 3, 491-498 · 9 pages; a new co-author; added to Theorem 3.2 a second part about the case of a trivial scaling group, and gave an alternative proof of one of the implications; to appear in the Bulletin of the London Mathematical Society
arxiv created 2017/02/20 · openalex publication_date 2017/03/29 · arxiv updated 2017/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We prove that amenability of a unitary co-representation U of a locally compact quantum group passes to unitary co-representations that weakly contain U. This generalizes a result of Bekka, and answers affirmatively a question of Bédos, Conti and Tuset. As a corollary, we extend to locally compact quantum groups a result of the first-named author, which characterizes amenability of a locally compact group G by nuclearity of the reduced group C ∗ -algebra C r ∗ ( G ) and an additional condition.