593 research outputs found
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 state for strongly connected graphs is
invariant under quantum automorphism group of the graph. For circulant graphs,
it is shown that the action of classical and quantum automorphism group
preserves only one of the KMS states occurring at the critical inverse
temperature. We also give an example of a graph C*-algebra having more than one
KMS state such that all of them are invariant under the action of classical
automorphism group of the graph, but there is a unique KMS state which is
invariant under the action of quantum automorphism group of the graph.Comment: 15 pages, 2 figure
An averaging trick for smooth actions of compact quantum groups on manifolds
We prove that, given any smooth action of a compact quantum group (in the
sense of \cite{rigidity}) on a compact smooth manifold satisfying some more
natural conditions, one can get a Riemannian structure on the manifold for
which the corresponding -valued inner product on the space of
one-forms is preserved by the action
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 isomorphic with a similar twist-deformation of the quantum
isometry group of the original (undeformed) spectral triple. This result
generalizes similar work by Bhowmick and Goswami for Rieffel-deformed spectral
triples in [Comm. Math. Phys. 285 (2009), 421-444, arXiv:0707.2648]
Quantum automorphism groups of -graphs
We formulate a notion of the quantum automorphism groups of -graphs. We
show that two isomorphic -graphs have isomorphic quantum automorphism groups
making the notion well-defined. We compute the quantum automorphism groups of a
few -graphs. It is observed that quantum automorphism group of a -graph
can be realized as the quantum automorphism group of a -graph.Comment: 17 PAGE
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