Normal Subgroups, Center and Inner Automorphisms of Compact Quantum Groups

2013/05/06 by Issan Patri, Patri, Issan
Mathematics · #46L89 (Primary) 20G42 #81R50 (Secondary) #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:20G42 #msc:46L89 #msc:81R50

paper · pdf · doi:10.48550/arxiv.1305.1080

32 pages

arxiv created 2013/05/06 · openalex publication_date 2013/05/06 · arxiv updated 2013/05/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce a class of automorphisms of compact quantum groups which may be thought of as inner automorphisms and explore the behaviour of normal subgroups of compact quantum groups under these automorphisms. We also define the notion of center of a compact quantum group and compute the center for several examples. We briefly touch upon the commutator subgroup of a compact quantum group and discuss how its relation with the center can be different from the classical case.

Related

• The canonical central exact sequence for locally compact quantum groups
• Topological automorphism groups of compact quantum groups
• Open quantum subgroups of locally compact quantum groups
• Notes on Compact Quantum Groups
• Unitary representations of compact quantum groups