Discrete subfactors, realization of algebra objects, and Q-system completion

Abstract: In recent decades, we have seen that quantum symmetries of quantum mathematical objects, like non-commutative spaces and quantum field theories, are best described by quantum groups, subfactors, and unitary tensor categories. Subfactor classification has led to discovery of interesting "exotic" quantum symmetries and to important constructions for unitary tensor categories. For example, Q-systems (special C* Frobnius algebra objects) were introduced by Longo to characterize the canonical endomorphism for type III subfactors, which is the analog of Jones' basic construction for type $II_1$ and Kosaki's version for type III. We will use this perspective to discuss some subfactor results which go beyond small index classification, making connections to quantum groups along the way. We'll then discuss a version of a unitary higher idempotent completion for C*/W* 2-categories based on Gaiotto-Johnson-Freyd's theory of condensations in higher categories.

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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