Non-existence of faithful isometric action of compact quantum groups on compact, connected Riemannian manifolds
Geometric and Functional Analysis
Suppose that a compact quantum group Q acts faithfully on a smooth, compact, connected manifold M, i.e. has a C* (co)-action α on C(M), such that the action α is isometric in the sense of [GOS09] for some Riemannian structure on M. We prove that Q must be commutative as a C* algebra i.e. Q≅ C(G) for some compact group G acting smoothly on M. In particular, the quantum isometry group of M (in the sense of [GOS09]) coincides with C(ISO(M)).
Goswami, Debashish and Joardar, Soumalya, "Non-existence of faithful isometric action of compact quantum groups on compact, connected Riemannian manifolds" (2018). Journal Articles. 1488.