Abstract Consider a Leibniz superalgebra L additionally graded by an arbitrary set I (set grading). We show that L decomposes as the sum of well-described graded ideals plus (maybe) a suitable linear subspace. In the case of L being of maximal length, the simplicity of L is also characterized in terms of connections.

中文翻译：

---

具有集合分级的莱布尼茨超代数

摘要 考虑由任意集合 I（集合分级）额外分级的莱布尼茨超代数 L。我们证明 L 分解为描述良好的分级理想加上（可能）一个合适的线性子空间的总和。在 L 为最大长度的情况下，L 的简单性也体现在连接方面。