Operator biflatness of the L¹-algebras of compact quantum groups

2013/01/10 by Martijn Caspers, Caspers, Martijn, Hun Hee Lee +3
Mathematics · #43A20 (Primary) 20G42 (Secondary) #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #math.FA #math.OA #msc:20G42 #msc:43A20

paper · pdf · doi:10.48550/arxiv.1301.2069

Minor updates. To appear in Crelle's journal

openalex publication_date 2013/01/10 · arxiv created 2013/04/08 · arxiv updated 2013/04/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the L¹-algebra of any non-Kac type compact quantum group does not satisfy operator biflatness. Since operator amenability implies operator biflatness, this result shows that any co-amenable, non-Kac type compact quantum group gives a counter example to the conjecture that L¹(\Gb) is operator amenable if and only if \Gb is amenable and co-amenable for any locally compact quantum group \Gb. The result also implies that the L¹-algebra of a locally compact quantum group is operator biprojective if and only if \Gb is compact and of Kac type.

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