Year: 2026
Type: preprint
Abstract: We give criteria for when finitely generated local modules over a commutative algebra $A$ in the ind-completion $\widehat{\mathcal{C}}$ of a braided tensor category $\mathcal{C}$ inherit the structure of a (rigid, braided, ribbon) tensor category. We then apply this to simple current algebras $A = \bigoplus_{g \in Γ} E_g$, where $Γ$ is a subgroup of invertible objects in $\mathcal{C}$. Using a description of simple $A$-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 $\mathfrak{gl}(1|1)$.
Source: arXiv (Cornell University)
Authors: Shimizu, Kenichi, Yadav, Harshit
Institutions: Shibaura Institute of Technology, University of Alberta
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7147387484
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