arXiv subjects

Soumalya Joardar

Publications and source records attributed to Soumalya Joardar.

27 records · Page 2Linked to original sources

arXiv2018

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.

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arXiv2018

Quantum symmetry of graph C*-algebras at 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 action in the sense of [11] and preserving the KMS state at critical inverse temperature. We show that this category for a certain KMS state at critical inverse temperature coincides with the category introduced in [11] for a class of graphs. We also introduce an orthogonal filtration on Cuntz algebra with respect to the unique KMS state and show that the category of CQG's preserving the orthogonal filtration coincides with the category introduced in this paper.

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arXiv2018

Non-existence of faithful isometric action of compact quantum groups on compact, connected Riemannian manifolds

Suppose that a compact quantum group $\clq$ 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 sense of \cite{Goswami} for some Riemannian structure on $M$. We prove that $\clq$ must be commutative as a $C^{\ast}$ algebra i.e. $\clq\cong C(G)$ 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 $C(ISO(M))$.

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arXiv2017

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 quantum automorphism group of underlying directed graph in the sense of T. banica is shown to be a quantum subgroup of quantum automorphism group in our sense. Quantum symmetries for some concrete graph C*-algebras have been computed.

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arXiv2015

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 a lift of the smooth action as a bimodule morphism on the bimodule of one forms has been deduced and it is also shown to be equivalent to the condition of preserving some Riemannian inner product on the manifold.

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arXiv2015

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 $C^\infty(M)$-valued inner product on the space of one-forms is preserved by the action.

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arXiv2014

Rigidity of action of compact quantum groups II

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 group is necessarily commutative as a C \ast algebra i.e. Q = C(G) for some compact group G. Using this, it is also proved that the quantum isometry group of Rieffel deformation of such manifold M must be a Rieffel-Wang deformation of C(ISO(M))

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arXiv2014

A note on geometric characterization of quantum isometries of classical manifolds

If a compact quantum group acts isometrically on a (possibly discon- nected) compact smooth Riemannian manifold such that the action commutes with the Laplacian then it is known that the differential of the action preserves Rieman- nian inner product on forms. In this note, we prove a partial converse to this, under the additional assumption that the manifold is ori- ented and the action preserves the orientation in a suitable sense. Using this an alternative line of arguments is given for proving that there is no quantum isometry for a compact, connected, Riemannian manifold.

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arXiv2014

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].

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