In this paper we describe finite-dimensional complex Leibniz superalgebras whose even part is the simple Leibniz algebra corresponding to \(\mathfrak {sl}_{2}\), i.e. its quotient algebra with respect to the Leibniz kernel I is isomorphic to \(\mathfrak {sl}_{2}\). We classify these Leibniz superalgebras in several cases with arbitrary dimensions in which the odd part is essentially a Leibniz irreducible \((\mathfrak {sl}_{2} \dotplus I)\)-module or a finite direct sum of them.

中文翻译：

---

关于具有等于$ 2 $ \ mathfrak {sl} _ {2} $的偶数部分的莱布尼兹超代数

在本文中，我们描述了有限维复Leibniz超代数，其偶数部分是对应于\（\ mathfrak {sl} _ {2} \）的简单Leibniz代数，即相对于Leibniz核I的商代数与\同构。 （\ mathfrak {sl} _ {2} \）。我们在几种情况下使用任意维数将这些莱布尼兹超代数分类，其中奇数部分本质上是莱布尼兹不可约\（（\ mathfrak {sl} _ {2} \ dotplus I）\）-模或它们的有限直接和。