Quantum Galois Group of Subfactors

Abstract: (joint work with Suvrajit Bhattacharjee and Alex Chirvasitu)

In this talk, I prove the existence of a universal (terminal) object in a number of categories of Hopf algebras acting on a given subfactor $N \subset M$ (finite index, type $\text{II}_1$) such that $N$ is in the fixed point subalgebra of the action. These universal Hopf algebras can be interpreted as a quantum group version of Galois group of the subfactor. We compute such universal quantum groups for certain class of subfactors, notably those coming from outer actions of finite dimensional Hopf $\ast$ algebras.

category theoryoperator algebrasquantum algebra

Audience: researchers in the topic

Quantum Groups Seminar [QGS]

Series comments: This 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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