二维预约当代数的Rota-Baxter算子  

Rota-Baxter Operators on Two-Dimensional Pre-Jordan Algebras

作　　者：王智斌 

机构地区：[1]辽宁师范大学数学学院,辽宁 大连

出　　处：《理论数学》2023年第11期3154-3164,共11页Pure Mathematics

摘　　要：本文主要计算二维预约当代数的Rota-Baxter算子,得到二维预约当代数上Rota-Baxter算子的完全分类。确定二维预约当代数对应的特殊的四维预约当代数的代数运算,构造这些特殊的四维预约当代数上JP-方程的解。最后利用二维预约当代数的Rota-Baxter算子构造二维的J-dendriform代数。This paper mainly calculates the Rota-Baxter operators on two-dimensional pre-Jordan algebras and obtains the complete classification of the Rota-Baxter operators on two-dimensional pre-Jordan algebras. The algebraic operations of special four-dimensional pre-Jordan algebras corresponding to two-dimensional pre-Jordan algebras are determined, and the solutions of JP-equations on these special four-dimensional pre-Jordan algebras are constructed. Finally, two-dimensional J-dendriform algebras are constructed using the Rota-Baxter operator of two-dimensional pre-Jordan algebras.

关 键 词：预约当代数 JP-方程 Rota-Baxter算子 

分 类 号：G63[文化科学—教育学]