约当三系上非零权的相对Rota-Baxter算子
Relative Rota-Baxter Operator of Non-Zero Weights on the Jordan Triple
摘要: 本文主要研究约当三系上关于非零权的相对Rota-Baxter算子。首先回顾了约当代数，约旦三系以及子系的概念，然后给出了约当三系的表示的定义，进而得出约当三系在另一个约当三系上作用的概念，以及约当三系上非零权的相对Rota-Baxter算子的定义，找到了在约当三系及其作用空间的直和上构造新约当三系的方法。最后，给出了在一个约当三系上定义与相对Rota-Baxter算子有关的新运算可得到新的约当三系的方法，并且构造了新的约当三系的表示。此外文中还给出了约当三系上构造相对Rota-Baxter算子的方法。
Abstract:
In this paper, we mainly study the relative Rota-Baxter operators on Jordan triple systems of non-zero weights. First, we recall the concepts of Jordan algebra, Jordan triple systems, and subsystems, and then the definition of the representation of Jordan triple systems is given. Then, the concept of Jordan triple systems acting on another Jordan triple system is obtained, as well as the definition of relative Rota-Baxter operators of nonzero weights on Jordan triple systems. A method for con-structing a new Jordan triple system on the direct sum of Jordan triple systems and their action spaces is found. Finally, it is shown that by defining new operations related to the relative Ro-ta-Baxter operator on a Jordan triple system, a new Jordan triple system can be obtained, and a new representation of the Jordan triple system is constructed. In addition, a method for constructing relative Rota-Baxter operators is also presented.
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