二维预约当代数的Rota-Baxter算子
Rota-Baxter Operators on Two-Dimensional Pre-Jordan Algebras
DOI: 10.12677/PM.2023.1311327, PDF,   
作者: 王智斌：辽宁师范大学数学学院，辽宁 大连
关键词: 预约当代数；JP-方程；Rota-Baxter算子；Pre-Jordan Algebra； JP-Equation； Rota-Baxter Operator
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。
Abstract: 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.
文章引用：王智斌. 二维预约当代数的Rota-Baxter算子[J]. 理论数学, 2023, 13(11): 3154-3164. https://doi.org/10.12677/PM.2023.1311327

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