发表机构
Northeast Normal University（东北师范大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文完成3维复诺维科夫-泊松代数的同构分类，以此证明除𝔰𝔩₂(ℂ)外的3维复转置泊松代数均可由其得到，且Sartayev猜想在3维情形成立。
AI 中文摘要
本文对3维复诺维科夫-泊松代数给出了同构意义下的完全分类。作为该分类的应用，进一步证明了除李代数𝔰𝔩₂(ℂ)外，所有3维复转置泊松代数均可由诺维科夫-泊松代数得到。因此，Sartayev猜想在3维情形成立，即所有3维复转置泊松代数作为GD代数时都是特殊的。
英文摘要
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.
Comments22 pages
