A modular fusion category 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 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.
Cite this article
Iordanis Romaidis, Ingo Runkel, Mapping class group representations and Morita classes of algebras. Quantum Topol. 14 (2023), no. 3, pp. 429–465DOI 10.4171/QT/192