Quantum graphs, subfactors and tensor categories

Abstract: We will introduce equivariant graphs with respect to a quantum symmetry along with examples such as classical graphs, Cayley graphs of finite groupoids, and their quantum analogues. These graphs can be presented concretely by modeling a quantum vertex set by an inclusion of operator algebras and the quantum edge set by an equivariant endomorphism, idempotent with respect to convolution/Schur product. Equipped with this viewpoint and tools from subfactor theory, we will see how to obtain all these idempotents using higher relative commutants and the quantum Fourier transform. Finally, we will state a quantum version of Frucht's Theorem, showing that every quasitriangular finite quantum groupoid arises as certain automorphisms of some categorified graph.

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.

The zoom links will be distributed by mail, so please join the mailing list if you are interested in attending the seminar.