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Rigidity of action of compact quantum groups on compact, connected manifolds
Suppose that a compact quantum group $\clq$ acts faithfully on a smooth, compact, connected manifold $M$ such that the action $\alpha$ is smooth, i.e. it leaves $C^\infty(M)$ invariant and the linear
A new look at Levi-Civita connection in noncommutative geometry
We prove the existence and uniqueness of Levi-Civita connections for a noncommutative pseudo-Riemannian metric on a class of centered bimodule of one forms. As an application, we compute the Ricci
Quantum symmetry of graph C∗-algebras associated with connected graphs
We define a notion of quantum automorphism groups of graph [Formula: see text]-algebras for finite, connected graphs. Under the assumption that the underlying graph does not have any multiple edge or
Quantum symmetry of graph $C^{\ast }$-algebras at\cr critical inverse temperature
We give a notion of quantum automorphism group of graph C*-algebras without sink at critical inverse temperature. This is defined to be the universal object of a category of CQG's having a linear
Quantum Isometry Groups of Noncommutative Manifolds Obtained by Deformation Using Dual Unitary 2-Cocycles ?
It is proved that the (volume and orientation-preserving) quantum isometry group of a spectral triple obtained by deformation by some dual unitary 2-cocycle is isomor- phic with a similar
Scalar curvature of a Levi-Civita connection on the Cuntz algebra with three generators
A differential calculus on the Cuntz algebra with three generators coming from the action of rotation group in three dimensions is introduced. The differential calculus is shown to satisfy
Non-existence of faithful isometric action of compact quantum groups on compact, connected Riemannian manifolds
Suppose that a compact quantum group $${\mathcal{Q}}$$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
An example of explicit dependence of quantum symmetry on KMS states
We compute all the quantum symmetries of a graph with n- disjoint loops at the critical inverse temperature. We show that the set of non-isomorphic CQG's appearing as quantum symmetry at the critical
Levi-Civita connections for conformally deformed metrics on tame differential calculi
Given a tame differential calculus over a noncommutative algebra [Formula: see text] and an [Formula: see text]-bilinear metric [Formula: see text] consider the conformal deformation [Formula: see
A note on the injectivity of actions of compact quantum groups on a class of $C^{\ast }$-algebras
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
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