Open quantum subgroups of locally compact quantum groups

2015/11/12 by Mehrdad Kalantar, Paweł Kasprzak, Kalantar, Mehrdad +3
Mathematics · #22D25 (Secondary) #46L89 (Primary) #FOS: Mathematics #Operator Algebras (math.OA) #math.OA #msc:22D25 #msc:46L89

paper · pdf · doi:10.48550/arxiv.1511.03952

30 pages, v2 simplifies the proof of Theorem 5.8 (and drops the properness assumption) as well as corrects several small points. The final version will appear in Advances in Mathematics

arxiv created 2016/08/12 · arxiv updated 2016/08/15

Abstract

The notion of an open quantum subgroup of a locally compact quantum group is introduced and given several equivalent characterizations in terms of group-like projections, inclusions of quantum group C*-algebras and properties of respective quantum homogenous spaces. Open quantum subgroups are shown to be closed in the sense of Vaes and normal open quantum subgroups are proved to be in 1-1 correspondence with normal compact quantum subgroups of the dual quantum group.

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