二维预泊松代数的分类
Classification of 2-Dimensional Pre-Poisson Algebras
摘要: 本文主要研究低维预泊松代数的分类，以二维Zinbiel代数的分类为基础，计算低维预泊松代数上的预李代数的左乘运算在某组基下对应的矩阵，确定了对应的预李代数的类型。最后，通过具体计算得到了预泊松代数的同构关系，从而得到了二维预泊松代数的分类。
Abstract:
This paper mainly studies the classification of low-dimensional pre-poisson algebras. Based on the classification of two-dimensional Zinbiel algebras, the matrix corresponding to the left multiplica-tion operation of the pre-poisson algebras on the low-dimensional pre-poisson algebras is calculated under a certain set of bases, and the type of the corresponding pre-poisson algebras is determined. Finally, the isomorphic relation of pre-poisson algebras is obtained through concrete calculation, and the classification of two-dimensional pre-poisson algebras is obtained.
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