Comparison of extensions of unitary VOAs and conformal nets

Abstract: In 2015, Carpi-Kawahigashi-Longo-Weiner (CKLW) initiated a systematic study of the relationship between unitary vertex operator algebras (UVOAs) and conformal nets (CNs). Building on their framework and Wassermann’s computation of the Connes fusion of modules of loop group SU(N) at positive integer levels, I showed in 2018 and 2020 that many rational UVOAs (including all WZW models) and their corresponding CNs have unitarily equivalent representation categories.

In this talk, I will show that when one considers extensions of UVOAs and CNs, the abstract equivalence of representation categories arising from the theory of Frobenius algebras and Q-systems is compatible with the unitary equivalences (in the line of CKLW and Wassermann) mentioned above.

operator 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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