Ribbon categories from ind-exact algebras: simple current case
Kenichi Shimizu, Harshit Yadav

TL;DR
This paper establishes criteria for local modules over certain algebras in braided tensor categories to inherit ribbon structures, and applies this to simple current algebras to produce new ribbon categories.
Contribution
It provides new conditions under which local modules over simple current algebras form ribbon tensor categories, with applications to quantum supergroup categories.
Findings
Criteria for local modules to inherit ribbon structures.
Verification of hypotheses for simple current algebras.
Construction of ribbon categories from quantum supergroups.
Abstract
We give criteria for when finitely generated local modules over a commutative algebra in the ind-completion of a braided tensor category inherit the structure of a (rigid, braided, ribbon) tensor category. We then apply this to simple current algebras , where is a subgroup of invertible objects in . Using a description of simple -modules, we verify the required hypotheses for this class of algebras and deduce rigidity, braided, ribbon, and non-degeneracy properties for their finitely generated local modules. As applications, we construct examples of ribbon tensor categories from quantum supergroup categories for unrolled .
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.
