Mapping class group representations and Morita classes of algebras

A modular fusion category \mathcal{C} allows one to define projective representations of the mapping class groups of closed surfaces of any genus. We show that if all these representations are irreducible, then \mathcal{C} has a unique Morita class of simple non-degenerate algebras, namely, that of...

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Bibliographic Details
Published inQuantum topology Vol. 14; no. 3; pp. 429 - 465
Main Authors Romaidis, Iordanis, Runkel, Ingo
Format Journal Article
LanguageEnglish
Published 01.01.2023
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Summary:A modular fusion category \mathcal{C} allows one to define projective representations of the mapping class groups of closed surfaces of any genus. We show that if all these representations are irreducible, then \mathcal{C} has a unique Morita class of simple non-degenerate algebras, namely, that of the tensor unit. This improves on a result by Andersen and Fjelstad, albeit under stronger assumptions. One motivation to look at this problem comes from questions in three-dimensional quantum gravity.
ISSN:1663-487X
1664-073X
DOI:10.4171/qt/192