Quantum automorphism groups of discrete structures

Abstract: Given any mathematical structure, it is a natural question to ask which quantum symmetries it admits. One can in general not hope to find a quantum automorphism group for any structure in the framework of Kustermans-Vaes, as a necessary condition for its existence is local compactness of the classical automorphism group. In recent work, a wide range of discrete structures, those which are connected and locally finite in a suitable sense, were shown to admit an algebraic quantum automorphism group. The main tool for their construction is a generalization of the Tannaka-Krein-Woronowicz reconstruction theorem. In particular, this allows to construct quantum automorphism groups of connected locally finite quantum graphs, such as Wasilewski's quantum Cayley graphs, generalizing joint results with Stefaan Vaes.

category theoryoperator algebrasquantum algebra

Audience: researchers in the topic

Quantum Groups Seminar [QGS]

Series comments: This online seminar aims to bring together experts in the area of quantum groups. The seminar topics will cover the theory of quantum groups and related structures in a large sense: Hopf algebras, operator algebras, q-deformations, higher categories and related branches of noncommutative mathematics.

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