论文标题
Leibniz代数有衍生
Leibniz algebras with derivations
论文作者
论文摘要
在本文中，我们考虑了带有派生的莱布尼兹代数。由Leibniz代数和区分推导组成的一对称为Leibder对。我们为Leibder对定义了具有代表性系数的同伴。我们研究了莱布对的中央扩展和阿贝尔扩展。在下一个中，我们将形式的变形理论概括为莱布对，其中我们将莱布尼兹支架和杰出的派生变形。它由莱布（Leibder）配对的共同体学本身与系数。最后，我们考虑在SH Leibniz代数上的同质派生和Leibniz $ 2 $ 2 $ - 代数的$ 2 $衍生。 $ 2 $ - 学期的SH Leibniz代数的类别与同型派生相当于Leibniz $ 2 $ -Algebras的类别，$ 2 $ - 代数。
In this paper, we consider Leibniz algebras with derivations. A pair consisting of a Leibniz algebra and a distinguished derivation is called a LeibDer pair. We define a cohomology theory for LeibDer pair with coefficients in a representation. We study central extensions and abelian extensions of a LeibDer pair. In the next, we generalize the formal deformation theory to LeibDer pairs in which we deform both the Leibniz bracket and the distinguished derivation. It is governed by the cohomology of LeibDer pair with coefficients in itself. Finally, we consider homotopy derivations on sh Leibniz algebras and $2$-derivations on Leibniz $2$-algebras. The category of $2$-term sh Leibniz algebras with homotopy derivations is equivalent to the category of Leibniz $2$-algebras with $2$-derivations.
