2013/11/29 by Sven Raum, Raum, Sven, Moritz Weber +1 · 2 citations
Mathematics · #16T30 #20G42 #46L54 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA) #Quantum Algebra (math.QA) #math.OA #math.QA #msc:16T30 #msc:20G42 #msc:46L54
paper · pdf · doi:10.48550/arxiv.1311.7630
26 pages; Relying on quantum group methods, this article extends the results presented in arXiv:1212.4742 considerably. The essence of the combinatorial approach used in arXiv:1212.4742 is presented in arXiv:1312.1497; v2: added a missing hypothesis to Theorem 3.1
openalex publication_date 2013/11/29 · arxiv created 2014/01/14 · arxiv updated 2014/01/15 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
We consider compact matrix quantum groups whose fundamental corepresentation matrix has entries which are partial isometries with central support. We show that such quantum groups have a simple representation as semi-direct product quantum groups of a group dual quantum group by an action of a permutation group. This general result allows us to completely classify easy quantum groups with the above property by certain reflection groups. We give four applications of our result. First, there are uncountably many easy quantum groups. Second, there are non-easy quantum groups between the free orthogonal quantum group and the permutation group. Third, we study operator algebraic properties of the hyperoctahedral series. Finally, we prove a generalised de Finetti theorem for easy quantum groups in the scope of this article.