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Suppose that a compact quantum group $clq$ acts faithfully on a smooth, compact, connected manifold $M$, i.e. has a $C^*$ (co)-action $alpha$ on $C(M)$, such that the action $alpha$ is isometric in the sense of cite{Goswami} for some Riemannian structure on $M$. We prove that $clq$ must be commutative as a $C^{ast}$ algebra i.e. $clqcong C(G)$ for some compact group $G$ acting smoothly on $M$. In particular, the quantum isometry group of $M$ (in the sense of cite{Goswami}) coincides with $C(ISO(M))$.
Suppose that a compact quantum group ${mathcal Q}$ acts faithfully on a smooth, compact, connected manifold $M$, i.e. has a $C^{ast}$ (co)-action $alpha$ on $C(M)$, such that $alpha(C^infty(M)) subseteq C^infty(M, {mathcal Q})$ and the linear span of
A general form of contractive idempotent functionals on coamenable locally compact quantum groups is obtained, generalising the result of Greenleaf on contractive measures on locally compact groups. The image of a convolution operator associated to a
We give some sufficient conditions for the injectivity of actions of compact quantum groups on $C^{ast}$-algebra. As an application, we prove that any faithful smooth action by a compact quantum group on a compact smooth (not necessarily connected) m
Correspondence between idempotent states and expected right-invariant subalgebras is extended to non-coamenable, non-unimodular locally compact quantum groups; in particular left convolution operators are shown to automatically preserve the right Haar weight.
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 grou