Geodesic
Equivariant $\textrm {C}^*$-correspondences and compact quantum group actions on Pimsner algebras
Canadian journal of mathematics, Tome 77 (2025) no. 1, pp. 57-96

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DOI

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.
DOI : 10.4153/S0008414X23000810
Mots-clés : C*-correspondences, Pimsner algebras, KMS states, compact quantum groups, graph C*-algebras 
Bhattacharjee, Suvrajit; Joardar, Soumalya. Equivariant $\textrm {C}^*$-correspondences and compact quantum group actions on Pimsner algebras. Canadian journal of mathematics, Tome 77 (2025) no. 1, pp. 57-96. doi: 10.4153/S0008414X23000810
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     title = {Equivariant $\textrm {C}^*$-correspondences and compact quantum group actions on {Pimsner} algebras},
     journal = {Canadian journal of mathematics},
     pages = {57--96},
     year = {2025},
     volume = {77},
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     doi = {10.4153/S0008414X23000810},
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