论文标题
三元莱布尼兹颜色代数及其他
Ternary Leibniz color algebras and beyond
论文作者
论文摘要
本文的目的是研究一些三元代数。我们将某些结果概括为三元代数的三元代数。为了产生莱布尼兹颜色代数的三元莱布尼兹颜色代数的示例，给出了莱布尼兹颜色代数的几个结果。接下来，我们介绍三元莱布尼兹颜色代数，并提供一些与操作员，直接总和和张量产品打交道的结构。之后，我们在三元Leibniz颜色代数上引入双模模，并指出在三元leibniz颜色代数上的两个双模块的直接总和和张量产物也是给出的biModule，这也是纪元的三元模块。然后，我们介绍三元莱布尼兹 - 波森颜色代数并研究其一些特性。最后，我们简要介绍了颜色谎言三重系统，颜色约旦三重系统和comstrans颜色代数。还研究了其中的连接。
The purpose of this paper is to study some Ternary color algebras. We generalize some results on ternary Leibniz algebras to the case of ternary Leibniz color algebras. In order to produce examples of ternary Leibniz color algebras from Leibniz color algebras, several results on Leibniz color algebras are given. Next, We introduce ternary Leibniz color algebras and give some constructions dealing with operators, direct sum and tensor product. After that, We introduce bimodule over ternary Leibniz color algebras and point out that the direct sum and the tensor product of two bimodules over a ternary Leibniz color algebras is also a bimodule over the given ternary Leibniz color algebra. Then, We introduce ternary Leibniz-Poisson color algebras and study some of their properties. Finally, we give a brief description of color Lie triple systems, color Jordan triple systems and Comstrans color algebras. The connections among them are also studied.
