论文标题
$ \ Mathcal {O} $ - Leibniz代数上的运算符和相关结构
$\mathcal{O}$-operators and related structures on Leibniz algebras
论文作者
论文摘要
$ \ Mathcal {O} $ - 运算符已通过其表示来扩展Leibniz代数。在本文中，我们调查了与莱布尼兹代数上的$ \ Mathcal {O} $ - 运算符有关的几个结构，并介绍（dual）$ \ Mathcal {o} $ n-N-N-N-N-N-N-N-N-n-ntrentures leibniz代数与其表示相关。事实证明，$ \ Mathcal {o} $ - 运算符和双重 $ \ MATHCAL {O} $ N-N-结构在某些条件下相互生成。还表明，在二元leibniz代数上，强的毛勒 - 卡丹方程式的解决方案产生了双$ \ Mathcal {o} $ n结构。最后，对Leibniz代数上的$ r-n $结构，RBN结构和$ \ Mathcal {B} n $结构进行了详尽的研究，并还研究了它们的相互依存关系。
An $\mathcal{O}$-operator has been used to extend a Leibniz algebra by its representation. In this paper, we investigate several structures related to $\mathcal{O}$-operators on Leibniz algebras and introduce (dual) $\mathcal{O}$N-structures on Leibniz algebras associated to their representations. It is proved that $\mathcal{O}$-operators and dual $\mathcal{O}$N-structures generate each other under certain conditions. It is also shown that a solution of the strong Maurer-Cartan equation on the twilled Leibniz algebra gives rise to a dual $\mathcal{O}$N-structure. Finally, $r-n$ structures, RBN-structures and $\mathcal{B}N$-structures on Leibniz algebras are thoroughly studied and their interdependent relations are also studied.
