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PreprintCC0arXiv

Classification of Novikov-Poisson Algebras and Their Applications

  • Ziyi Zhang
  • Zeyu Hao
  • Yining Sun
  • Liangyun Chen
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Abstract

In this paper, we give a complete classification, up to isomorphism, of 3-dimensional complex Novikov--Poisson algebras. As an application of the classification, we further prove that every 3-dimensional complex transposed Poisson algebra can be obtained from a Novikov--Poisson algebra except the Lie algebra sl2(ℂ). Consequently, Sartayev's conjecture holds in dimension 3, that is, every 3-dimensional complex transposed Poisson algebra is special when regarded as a GD algebra.

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Cite

BibTeXRIS
BibTeX
@misc{zhang2026classification,
  title = {{Classification of Novikov-Poisson Algebras and Their Applications}},
  author = {Ziyi Zhang and Zeyu Hao and Yining Sun and Liangyun Chen},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.28686},
  eprint = {2608.28686},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.28686},
  note = {CC0},
}
RIS
TY  - UNPB
TI  - Classification of Novikov-Poisson Algebras and Their Applications
AU  - Ziyi Zhang
AU  - Zeyu Hao
AU  - Yining Sun
AU  - Liangyun Chen
PY  - 2026
DA  - 2026/08/26
PB  - arXiv
DO  - 10.48550/arxiv.2608.28686
UR  - https://arxiv.org/abs/2608.28686
AB  - In this paper, we give a complete classification, up to isomorphism, of 3-dimensional complex Novikov--Poisson algebras. As an application of the classification, we further prove that every 3-dimensional complex transposed Poisson algebra can be obtained from a Novikov--Poisson algebra except the Lie algebra sl_2(ℂ). Consequently, Sartayev's conjecture holds in dimension 3, that is, every 3-dimensional complex transposed Poisson algebra is special when regarded as a GD algebra.
ER  -