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A dual theory of twisted Zhu's theory

  • Hao Wang
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Abstract

The notion of admissible g-twisted V-comodules is investigated for a graded vertex operator coalgebra V and a finite order automorphism g∈ Aut V. We prove that ℳ is an admissible g-twisted V-comodule if and only if its graded dual ℳ' is an admissible g−1-twisted V'-module for vertex operator algebra V'. Then we establish a dual theory of twisted Zhu's theory, i.e., there is a coassociative coalgebra Cg(V) for a graded vertex operator coalgebra V, any admissible g-twisted V-comodule gives a Cg(V)-comodule, and vice versa. We also prove that V is g-corational, which means every admissible g-twisted V-comodule is completely reducible, if and only if its dual vertex operator algebra V' is g-rational.

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Cite

BibTeXRIS
BibTeX
@misc{wang2026dual,
  title = {{A dual theory of twisted Zhu's theory}},
  author = {Hao Wang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.07203},
  eprint = {2609.07203},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.07203},
}
RIS
TY  - UNPB
TI  - A dual theory of twisted Zhu's theory
AU  - Hao Wang
PY  - 2026
DA  - 2026/09/07
PB  - arXiv
DO  - 10.48550/arxiv.2609.07203
UR  - https://arxiv.org/abs/2609.07203
AB  - The notion of admissible g-twisted V-comodules is investigated for a graded vertex operator coalgebra V and a finite order automorphism g∈ Aut V. We prove that ℳ is an admissible g-twisted V-comodule if and only if its graded dual ℳ' is an admissible g^−1-twisted V'-module for vertex operator algebra V'. Then we establish a dual theory of twisted Zhu's theory, i.e., there is a coassociative coalgebra C_g(V) for a graded vertex operator coalgebra V, any admissible g-twisted V-comodule gives a C_g(V)-comodule, and vice versa. We also prove that V is g-corational, which means every admissible g-twisted V-comodule is completely reducible, if and only if its dual vertex operator algebra V' is g-rational.
ER  -