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Classification and C2-cofiniteness of rational vertex operator algebras generated in low conformal weights

  • Jiancai Sun
  • Ruochen Yang
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Abstract

We obtain classification results for rational vertex operator algebras generated in low conformal weights. More precisely, we prove that every rational vertex operator algebra of OZ type strongly generated by its conformal weight two subspace V2 is isomorphic to a finite tensor product of Virasoro minimal models. We also prove that every rational vertex operator algebra of CFT type generated as a vertex algebra by its conformal weight one subspace V1 is isomorphic to a finite tensor product of simple affine vertex operator algebras associated with finite-dimensional simple Lie algebras at positive integral levels. Consequently, Zhu's conjecture that rationality implies C2-cofiniteness holds for both classes, and every such rational vertex operator algebra is regular.

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Cite

BibTeXRIS
BibTeX
@misc{sun2026classification,
  title = {{Classification and $C_2$-cofiniteness of rational vertex operator algebras generated in low conformal weights}},
  author = {Jiancai Sun and Ruochen Yang},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.06983},
  eprint = {2611.06983},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.06983},
}
RIS
TY  - UNPB
TI  - Classification and C_2-cofiniteness of rational vertex operator algebras generated in low conformal weights
AU  - Jiancai Sun
AU  - Ruochen Yang
PY  - 2026
DA  - 2026/11/04
PB  - arXiv
DO  - 10.48550/arxiv.2611.06983
UR  - https://arxiv.org/abs/2611.06983
AB  - We obtain classification results for rational vertex operator algebras generated in low conformal weights. More precisely, we prove that every rational vertex operator algebra of OZ type strongly generated by its conformal weight two subspace V_2 is isomorphic to a finite tensor product of Virasoro minimal models. We also prove that every rational vertex operator algebra of CFT type generated as a vertex algebra by its conformal weight one subspace V_1 is isomorphic to a finite tensor product of simple affine vertex operator algebras associated with finite-dimensional simple Lie algebras at positive integral levels. Consequently, Zhu's conjecture that rationality implies C_2-cofiniteness holds for both classes, and every such rational vertex operator algebra is regular.
ER  -