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The geometric classification of Novikov-Poisson and Gelfand-Dorfman algebras

  • Zeyu Hao
  • Ivan Kaygorodov
  • Azamat Saydaliyev
  • Ziyi Zhang
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Abstract

We give the geometric classification of complex 3-dimensional Novikov-Poisson and Gelfand-Dorfman algebras. In particular, we prove that the variety of complex 3-dimensional Novikov-Poisson algebras is 12-dimensional; it has 4 irreducible components and has no rigid algebras; the variety of complex 3-dimensional Gelfand-Dorfman algebras is 11-dimensional; it has 10 irreducible components and has 3 rigid algebras. As an additional result, we have the geometric classification of complex 3-dimensional Novikov algebras: it is 9-dimensional, and it has $4$ irreducible components with one rigid algebra.

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Cite

BibTeXRIS
BibTeX
@misc{hao2026geometric,
  title = {{The geometric classification of Novikov-Poisson and Gelfand-Dorfman algebras}},
  author = {Zeyu Hao and Ivan Kaygorodov and Azamat Saydaliyev and Ziyi Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.14010},
  eprint = {2610.14010},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.14010},
}
RIS
TY  - UNPB
TI  - The geometric classification of Novikov-Poisson and Gelfand-Dorfman algebras
AU  - Zeyu Hao
AU  - Ivan Kaygorodov
AU  - Azamat Saydaliyev
AU  - Ziyi Zhang
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2610.14010
UR  - https://arxiv.org/abs/2610.14010
AB  - We give the geometric classification of complex 3-dimensional Novikov-Poisson and Gelfand-Dorfman algebras. In particular, we prove that the variety of complex 3-dimensional Novikov-Poisson algebras is 12-dimensional; it has 4 irreducible components and has no rigid algebras; the variety of complex 3-dimensional Gelfand-Dorfman algebras is 11-dimensional; it has 10 irreducible components and has 3 rigid algebras. As an additional result, we have the geometric classification of complex 3-dimensional Novikov algebras: it is 9-dimensional, and it has $4$ irreducible components with one rigid algebra.
ER  -