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arXiv · 1410.8650

A note on geometric characterization of quantum isometries of classical manifolds

Debashish Goswami·Soumalya Joardar
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Abstract

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.

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Debashish Goswami, Soumalya Joardar. 2014-10-31. A note on geometric characterization of quantum isometries of classical manifolds. https://arxiv.org/abs/1410.8650

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