Invariant subsets under compact quantum group actions

2012/10/21 by Huichi Huang, Huang, Huichi · 2 citations
Mathematics · Physics and Astronomy · #16W22 (Secondary) #46L65 (Primary) #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Noncommutative and Quantum Gravity Theories #Operator Algebras (math.OA) #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.1210.5782

openalex publication_date 2012/10/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate compact quantum group actions on unital C^*-algebras by analyzing invariant subsets and invariant states. In particular, we come up with the concept of compact quantum group orbits and use it to show that countable compact metrizable spaces with infinitely many points are not quantum homogeneous spaces.

Citations

• Rigidity of action of compact quantum groups III: the general case

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• Discrete quantum group coaction on the circle
• Quantum Isometry group of dual of finitely generated discrete groups and quantum groups

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