2017/10/24 by Moritz Weber, Weber, Moritz · 1 citation
Mathematics · #05A18 #05E10 (Secondary) #20G42 #46LXX (Primary) #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Operator Algebras (math.OA) #Quantum Algebra (math.QA) #math.CO #math.OA #math.QA #msc:05A18 #msc:05E10 #msc:20G42 #msc:46LXX
paper · pdf · doi:10.48550/arxiv.1710.08662
27 pages; continuation of arxiv:1710.06199
arxiv created 2017/10/24 · openalex publication_date 2017/10/24 · arxiv updated 2017/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In a recent article, we gave a definition of partition C*-algebras. These are universal C*-algebras based on algebraic relations which are induced from partitions of sets. In this follow up article, we show that often we can associate a Hopf algebra structure to partition C*-algebras, and also a compact matrix quantum group structure. This follows the lines of Banica and Speicher's approach to quantum groups; however, we access them in a more algebraic way circumventing Tannaka-Krein duality. We give criteria when these quantum groups are quantum subgroups of Wang's free orthogonal quantum group. As a consequence, we see that even if we start with (generalized) categories of partitions which do not contain the pair partitions, in many cases we do not go beyond the class of Banica-Speicher quantum groups (aka easy quantum groups). However, we also discuss possible non-unitary Banica-Speicher quantum groups.