Strongly 1-Bounded Quantum Group von Neumann Algebras

Abstract: Strong $1$-boundedness is a property for a tracial von Neumann algebra $M$ that was introduced by Jung that allows one to distinguish $M$ from the (interpolated) free group factors. Many examples came from group von Neumann algebras, such as those from certain groups having property (T). For quantum group von Neumann algebras, Brannan and Vergnioux showed in a landmark paper that those coming from the orthogonal free quantum groups are strongly $1$-bounded, despite sharing many structural properties with the free group factors. We first review these developments, and then report on recent progress concerning permanence of strong $1$-boundedness under finite index subfactors and applications to quantum automorphism groups such as the quantum permutation group $S_{N^2}^+$. This last part is based on ongoing joint work with Brannan, Harris, and Yamashita.

operator algebrasquantum algebra

Audience: researchers in the topic

Comments: Note the unusual day and time!

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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.

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

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