二维转置预泊松代数的分类

Classification of 2-Dimensional Transposed Pre-Poisson Algebras

摘要: 随着二维Zinbiel代数，预李代数分类结果的完成，在转置泊松代数的研究基础上，本文研究了二维转置预泊松代数的分类以及转置预泊松代数与转置泊松代数的关系。首先利用二维Zinbiel代数的分类结果，取定转置预泊松代数上的Zinbiel代数，计算在这个条件下二维转置预泊松代数上预李代数的左乘运算，确定预李代数的类型。通过具体计算讨论二维的转置预泊松代数在同构意义下的分类。

Abstract: With the completion of the classification of 2-dimensional Zinbiel algebras and pre-lie algebras, based on the study of transposed Poisson algebras, in this paper, the classification of two-dimensional transposed pre-poisson algebras and the relationship between transposed pre-poisson algebras and transposed Poisson algebras are studied. First, by using the classification results of 2-dimensional Zinbiel algebras, we determine the Zinbiel algebras on transposed pre-poisson algebras, under these conditions, the left multiplication of pre-Lie algebras on two-dimensional transposed pre-poisson algebras is calculated, and the type of pre-Lie algebras is determined. The classification of two-dimensional transposed pre-poisson algebras in isomorphic sense is discussed by concrete calculation.