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arXiv · 2608.28686

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 $\mathfrak{sl}_2(\mathbb C)$. 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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Ziyi Zhang, Zeyu Hao, Yining Sun, Liangyun Chen. 2026-08-26. Classification of Novikov-Poisson Algebras and Their Applications. https://arxiv.org/abs/2608.28686

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