2023/01/31 by J. P. McCarthy, McCarthy, J. P.
Mathematics · #46L30 #46L67 #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA) #Quantum Algebra (math.QA) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2301.13423
openalex publication_date 2023/01/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Woronowicz proved the existence of the Haar state for compact quantum groups under a separability assumption later removed by Van Daele in a new existence proof. A minor adaptation of Van Daele's proof yields an idempotent state in any non-empty weak*-compact convolution-closed convex subset of the state space. Such subsets, and their associated idempotent states, are studied in the case of quantum permutation groups.