Rigidity of action of compact quantum groups II

2012/06/08 by Biswarup Das, B. Krishna Das, Debashish Goswami +4
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics #Noncommutative and Quantum Gravity Theories #Operator Algebras (math.OA) #Quantum Algebra (math.QA) #math.DG #math.OA #math.QA

paper · pdf · doi:10.48550/arxiv.1206.1718

Withdrawn because its content is now subsumed (with improvement) in arXiv:1309.1294 and arXiv:1410.8650

openalex publication_date 2012/06/08 · arxiv created 2014/11/14 · arxiv updated 2014/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Suppose that a compact quantum group Q acts faithfully and isomet- rically (in the sense of [10]) on a smooth compact, oriented, connected Riemannian manifold M . If the manifold is stably parallelizable then it is shown that the compact quantum group is necessarily commutative as a C ∗ algebra i.e. Q = C(G) for some compact group G. Using this, it is also proved that the quantum isometry group of Rieffel deformation of such manifold M must be a Rieffel-Wang deformation of C(ISO(M))

Citations

• Notes on Compact Quantum Groups
• Non-existence of faithful isometric action of compact quantum groups on\n compact, connected Riemannian manifolds
• A note on geometric characterization of quantum isometries of classical manifolds

Related

• Rigidity of action of compact quantum groups III: the general case
• Non-existence of faithful isometric action of compact quantum groups on\n compact, connected Riemannian manifolds
• A note on geometric characterization of quantum isometries of classical manifolds
• A note on the injectivity of action by compact quantum groups on a class of C^∗-algebras
• Smooth actions of compact quantum groups on compact smooth manifolds