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PreprintCC0arXiv

Classification of compatible left-symmetric conformal algebras on solvable Lie conformal algebras of rank two

  • Yuanmeng Zhai
  • Yanyong Hong
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Abstract

In this paper, we give a complete classification of compatible left-symmetric conformal algebra structures on solvable Lie conformal algebras which are free of rank two as ℂ[∂]-modules up to isomorphism. We obtain ten mutually non-isomorphic normal-form types and determine the precise equivalence relations among the parameters within each family. Moreover, we also characterize the Novikov conformal algebras among the classified left-symmetric conformal algebras, thereby obtaining a complete classification of compatible Novikov conformal algebra structures in the same setting.

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Cite

BibTeXRIS
BibTeX
@misc{zhai2026classification,
  title = {{Classification of compatible left-symmetric conformal algebras on solvable Lie conformal algebras of rank two}},
  author = {Yuanmeng Zhai and Yanyong Hong},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.30471},
  eprint = {2610.30471},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.30471},
  note = {CC0},
}
RIS
TY  - UNPB
TI  - Classification of compatible left-symmetric conformal algebras on solvable Lie conformal algebras of rank two
AU  - Yuanmeng Zhai
AU  - Yanyong Hong
PY  - 2026
DA  - 2026/10/21
PB  - arXiv
DO  - 10.48550/arxiv.2610.30471
UR  - https://arxiv.org/abs/2610.30471
AB  - In this paper, we give a complete classification of compatible left-symmetric conformal algebra structures on solvable Lie conformal algebras which are free of rank two as ℂ[∂]-modules up to isomorphism. We obtain ten mutually non-isomorphic normal-form types and determine the precise equivalence relations among the parameters within each family. Moreover, we also characterize the Novikov conformal algebras among the classified left-symmetric conformal algebras, thereby obtaining a complete classification of compatible Novikov conformal algebra structures in the same setting.
ER  -