论文标题
对称的Zinbiel超级甲壳虫
Symmetric Zinbiel superalgebras
论文作者
论文摘要
引入了对称的Zinbiel超级甲壳虫的概念。我们证明，对称Zinbiel Superalgebra的nilpotency指数不大于4，并描述了两个生成的对称的Zinbiel代数和奇数产生的超甲虫。我们讨论单声道和二元对称Zinbiel和Leibniz代数的身份。事实证明，每个二次Zinbiel代数都是2步的nilpotent。此外，我们研究对称Zinbiel代数的双重扩展。
The notion of symmetric Zinbiel superalgebras is introduced. We prove that the nilpotency index of a symmetric Zinbiel superalgebra is not greater than 4 and describe two-generated symmetric Zinbiel algebras and odd generated superalgebras. We discuss identities of mono and binary symmetric Zinbiel and Leibniz algebras. It is proven that each quadratic Zinbiel algebra is 2-step nilpotent. Also, we study double extensions of symmetric Zinbiel algebras.
