Mapping class group representations and Morita classes of algebras
Quantum Algebra
2021-06-08 v2 High Energy Physics - Theory
Geometric Topology
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.
Keywords
Cite
@article{arxiv.2106.01454,
title = {Mapping class group representations and Morita classes of algebras},
author = {Iordanis Romaidis and Ingo Runkel},
journal= {arXiv preprint arXiv:2106.01454},
year = {2021}
}
Comments
32 pages, v2: corrected the level shift of sl(2), adapted Example 5.3