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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 linearExpand
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Quantum Symmetry of Graph C*-algebras associated with connected Graphs
We define a notion of quantum automorphism group of Graph C*-algebras for finite, connected graphs. Under the assumption that the underlying graph does not have any multiple edge or loop, the quantumExpand
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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 criticalExpand
Levi-Civita connections for conformally deformed metrics on tame differential calculi
Given a tame differential calculus over a noncommutative algebra A and an A-bilinear pseudoRiemannian metric g0, consider the conformal deformation g = k.g0, k being an invertible element of A. WeExpand
A note on the injectivity of action by 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 quantumExpand
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Smooth actions of compact quantum groups on compact smooth manifolds
Definition of a smooth action of a CQG on a compact, smooth manifold is given and studied. It is shown that a smooth action is always injective. Furthermore A necessary and sufficient condition for aExpand
Invariance of KMS states on graph C*-algebras under classical and quantum symmetry
We study invariance of KMS states on graph C*-algebras coming from strongly connected and circulant graphs under the classical and quantum symmetry of the graphs. We show that the unique KMS stateExpand
Improved bound on the non zero eigenvalues of the graph Laplacian coming from quantum symmetry of vertex transitive graphs
A chain of quantum subgroups of the quantum automorphism group of finite graphs has been introduced. It generalizes the construction of J. Bichon (see [3]) in a sense. A better bound of the non zeroExpand
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 RicciExpand
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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 similarExpand
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