A finiteness property for braided fusion categories
Deepak Naidu, Eric C. Rowell
TL;DR
This paper introduces a finiteness property for braided fusion categories, explores a conjecture characterizing such categories, and verifies the conjecture in key cases, linking it to categories with integral Frobenius-Perron dimension.
Contribution
It defines a new finiteness property for braided fusion categories and proposes a conjecture linking this property to integral Frobenius-Perron dimension categories.
Findings
Categories with property F have braid group representations factoring over finite groups
The conjecture holds in several important cases
Categories with integral Frobenius-Perron dimension are characterized by property F
Abstract
We introduce a finiteness property for braided fusion categories, describe a conjecture that would characterize categories possessing this, and verify the conjecture in a number of important cases. In particular we say a category has F if the associated braid group representations factor over a finite group, and suggest that categories of integral Frobenius-Perron dimension are precisely those with property F.
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
TopicsAlgebraic structures and combinatorial models · Nonlinear Waves and Solitons · Homotopy and Cohomology in Algebraic Topology