Quantum Symmetries of the Twisted Tensor Products of C*-Algebras

Bhowmick, Jyotishman; Mandal, Arnab; Roy, Sutanu; Skalski, Adam

doi:10.1007/s00220-018-3279-5

Cited by 2 publications

(2 citation statements)

References 44 publications

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“…3 contact with Connes' enterprise, resulted, following Wang's pioneering work on quantum symmetries of finite spaces [Wan98], in several constructions and insights. Let us mention, albeit incompletely, the work of: • Banica, Bichon, and collaborators on quantum symmetries of discrete structures (see [Ban05a,Ban05b,Bic03]); • Goswami, Bhowmick, and collaborators on quantum isometries of spectral triples (see [BG09, BG19, GJ18, Gos20]); • Banica, Skalski, and collaborators on quantum symmetries of C * -algebras equipped with orthogonal filtrations (see [BMRS19,BS13]); and • more recently, Goswami and collaborators on quantum symmetries of subfactors (see [BCG22]). The study of quantum symmetries of C * -algebras have also been rewarding enough.…”

Section: Compact Quantum Group Actions On Pimsner Algebrasmentioning

confidence: 99%

Equivariant -correspondences and compact quantum group actions on Pimsner algebras

Bhattacharjee,

Joardar

2023

Can. J. Math.-J. Can. Math.

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Let G be a compact quantum group. We show that given a G-equivariant $\textrm {C}^*$ -correspondence E, the Pimsner algebra $\mathcal {O}_E$ can be naturally made into a G- $\textrm {C}^*$ -algebra. We also provide sufficient conditions under which it is guaranteed that a G-action on the Pimsner algebra $\mathcal {O}_E$ arises in this way, in a suitable precise sense. When G is of Kac type, a KMS state on the Pimsner algebra, arising from a quasi-free dynamics, is G-equivariant if and only if the tracial state obtained from restricting it to the coefficient algebra is G-equivariant, under a natural condition. We apply these results to the situation when the $\textrm {C}^*$ -correspondence is obtained from a finite, directed graph and draw various conclusions on the quantum automorphism groups of such graphs, both in the sense of Banica and Bichon.

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Section: Compact Quantum Group Actions On Pimsner Algebrasmentioning

confidence: 99%

Equivariant -correspondences and compact quantum group actions on Pimsner algebras

Bhattacharjee,

Joardar

2023

Can. J. Math.-J. Can. Math.

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“…(1) Banica, Bichon and collaborators on quantum symmetries of discrete structures, see [Ban05a,Ban05b,Bic03]; (2) Goswami, Bhowmick and collaborators on quantum isometries of spectral triples, see [BG10, Gos20, GJ18, BG19, BG09, BBG21]; (3) Banica, Skalski and collaborators on quantum symmetries of C * -algebras equipped with orthogonal filtrations, see [BS13,BMRS19,TdC14]; (4) and more recently, Goswami and collaborators on quantum symmetries of subfactors, see [BCG22,HG21].…”

Section: Introductionmentioning

confidence: 99%

Braided quantum symmetries of graph $\mathrm{C}^*$-algebras

Bhattacharjee¹,

Joardar²,

Roy³

2022

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We prove the existence of a universal braided compact quantum group acting on a graph C * -algebra in the category of T-C * -algebras with a twisted monoidal structure, in the spirit of the seminal work of S. Wang. To achieve this, we construct a braided analogue of the free unitary quantum group and study its bosonization. As a concrete example, we compute this universal braided compact quantum group for the Cuntz algebra.

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Quantum Symmetries of the Twisted Tensor Products of C*-Algebras

Cited by 2 publications

References 44 publications

Equivariant -correspondences and compact quantum group actions on Pimsner algebras

Equivariant -correspondences and compact quantum group actions on Pimsner algebras

Braided quantum symmetries of graph $\mathrm{C}^*$-algebras

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