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arXiv · 2106.01454

Mapping class group representations and Morita classes of algebras

Iordanis Romaidis·Ingo Runkel
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Abstract

A modular fusion category 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 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.

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Iordanis Romaidis, Ingo Runkel. 2021-06-02. Mapping class group representations and Morita classes of algebras. https://arxiv.org/abs/2106.01454

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