Symmetries, quantizations, and duality

Abstract: In the talk, we are going to quantize several aspects of Cayley graphs. First, we are going to study quantum symmetries of Cayley graphs of abelian groups. From the classical theory, it is known that the Fourier transform diagonalizes the adjacency matrix of any such Cayley graph. This can be used to determine the graph's quantum automorphism group. Secondly, we are going to show, how to quantize Cayley graphs of abelian groups. We obtain a quantum graph by twisting the function algebra of the classical one. Finally, we recall a classical construction that takes a distance regular Cayley graph of an abelian group or, more generally, a translation association scheme and constructs its dual by applying the Fourier transform. We generalize this construction replacing abelian groups by arbitrary finite quantum groups.

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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