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PreprintCC BY 4.0arXiv

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≤Aut(V) a finite group. We prove Huang's conjecture that the categories of g-twisted V-modules, for g∈ 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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Cite

BibTeXRIS
BibTeX
@misc{xu2026gcrossed,
  title = {{$G$-crossed braided tensor categories of twisted modules}},
  author = {Shun Xu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.29130},
  eprint = {2610.29130},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.29130},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - G-crossed braided tensor categories of twisted modules
AU  - Shun Xu
PY  - 2026
DA  - 2026/10/21
PB  - arXiv
DO  - 10.48550/arxiv.2610.29130
UR  - https://arxiv.org/abs/2610.29130
AB  - Let V be a strongly rational vertex operator algebra and G≤Aut(V) a finite group. We prove Huang's conjecture that the categories of g-twisted V-modules, for g∈ 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.
ER  -