Non-existence of genuine (compact) quantum symmetries of compact, connected smooth manifolds
Advances in Mathematics
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 α(C∞(M))⊆C∞(M,Q) and the linear span of α(C∞(M))(1⊗Q) is dense in C∞(M,Q) with respect to the Fréchet topology. It was conjectured by the author quite a few years ago that Q must be commutative as a C⁎ algebra i.e. Q≅C(G) for some compact group G acting smoothly on M. The goal of this paper is to prove the truth of this conjecture. A remarkable aspect of the proof is the use of probabilistic techniques involving Brownian stopping time.
Goswami, Debashish, "Non-existence of genuine (compact) quantum symmetries of compact, connected smooth manifolds" (2020). Journal Articles. 173.