Mapping class group representations and Morita classes of algebras
Iordanis Romaidis, Ingo Runkel

TL;DR
This paper investigates the relationship between modular fusion categories and mapping class group representations, showing that irreducibility implies a unique Morita class of simple non-degenerate algebras, with implications for quantum gravity.
Contribution
It proves that irreducible mapping class group representations in certain categories imply a unique Morita class of algebras, strengthening previous results under stricter conditions.
Findings
Irreducible representations imply a unique Morita class of algebras.
The result improves upon previous work by Andersen and Fjelstad.
Motivated by questions in three-dimensional quantum gravity.
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Advanced Algebra and Geometry
