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arXiv · 2610.29130

$G$-crossed braided tensor categories of twisted modules

Shun Xu
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Abstract

Let $V$ be a strongly rational vertex operator algebra and $G\leq\operatorname{Aut}(V)$ a finite group. We prove Huang's conjecture that the categories of $g$-twisted $V$-modules, for $g\in G$, form a $G$-crossed braided fusion category. This category is faithfully $G$-graded, with tensor products representing the complete twisted intertwining operators of Du-Huang, the canonical pullback $G$-action, and crossed braiding. In particular, the associativity, coherence and rigidity required by the conjecture all hold.

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Shun Xu. 2026-10-21. $G$-crossed braided tensor categories of twisted modules. https://arxiv.org/abs/2610.29130

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