Compact quantum group structures on type-I C^*-algebras

2020/08/09 by Alexandru Chirvăsitu, Jacek Krajczok, Chirvasitu, Alexandru +3
Mathematics · #20G42 #46L85 #46L89 #Advanced Banach Space Theory #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.2008.03772

openalex publication_date 2020/08/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a number of results having to do with equipping type-I C^*-algebras with compact quantum group structures, the two main ones being that such a compact quantum group is necessarily co-amenable, and that if the C^*-algebra in question is an extension of a non-zero finite direct sum of elementary C^*-algebras by a commutative unital C^*-algebra then it must be finite-dimensional.

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