Solvability of a class of braided fusion categories
Sonia Natale, Julia Yael Plavnik
TL;DR
This paper proves that certain weakly integral braided fusion categories with simple objects of small Frobenius-Perron dimension are solvable and, in some cases, group-theoretical, advancing understanding of their algebraic structure.
Contribution
It establishes solvability for a class of braided fusion categories with bounded simple object dimensions and characterizes when they are group-theoretical.
Findings
Categories with simple objects of FP dimension ≤ 2 are solvable.
Such categories are group-theoretical if their universal grading group is trivial.
Provides structural insights into the classification of braided fusion categories.
Abstract
We show that a weakly integral braided fusion category C such that every simple object of C has Frobenius-Perron dimension at most 2 is solvable. In addition, we prove that such a fusion category is group-theoretical in the extreme case where the universal grading group of C is trivial.
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.