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Wydział Matematyki, Informatyki i Mechaniki Uniwersytetu Warszawskiego

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2023-05-17 17:15

Let G be a compact quantum group. Then upon introducing the notion of a G-equivariant C*-correspondence and a G-C*-algebra, we shall show that a G-equivariant C*-correspondence makes the associated Pimsner algebra a G-C*-algebra. Moreover, for a Kac-type compact quantum group G, under a natural condition, the corresponding G-action on the Pimsner algebra preserves the KMS state coming from a quasi-free dynamics if and only if it preserves the restriction of the KMS state to the coefficient C*-algebra of the C*-correspondence. We shall apply these results to the C*-correspondence coming from a finite directed graph without sources to understand the connection between the quantum symmetry of graph C*-algebras and their underlying graphs. This talk is based on a recently arXived joint work with Suvrajit Bhattacharjee.