2014/10/31 by Debashish Goswami, Goswami, Debashish, Soumalya Joardar +1
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Operator Algebras (math.OA) #math.OA
paper · pdf · doi:10.48550/arxiv.1410.8650
18 pages. arXiv admin note: substantial text overlap with arXiv:1309.1294
arxiv created 2014/10/31 · openalex publication_date 2014/10/31 · arxiv updated 2014/11/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
If a compact quantum group acts isometrically on a (possibly discon- nected) compact smooth Riemannian manifold such that the action commutes with the Laplacian then it is known that the differential of the action preserves Rieman- nian inner product on forms. In this note, we prove a partial converse to this, under the additional assumption that the manifold is ori- ented and the action preserves the orientation in a suitable sense. Using this an alternative line of arguments is given for proving that there is no quantum isometry for a compact, connected, Riemannian manifold.