Work

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

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.14010

Authors: Hao, Zeyu, Kaygorodov, Ivan, Saydaliyev, Azamat, Zhang, Ziyi

Institutions: Northeast Normal University, University of Beira Interior, Centro de Matemática e Aplicações, Academy of Sciences Republic of Uzbekistan

Language: English

Topic: Advanced Topics in Algebra

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Fundação para a Ciência e a Tecnologia

Awards: Centro de Matemática e Aplicações da Universidade da Beira Interior, G8550290551

OpenAlex ID: W7221797492

Cites: 3

Cited by:

Related to: 10