Some Theorems on Leibniz n-Algebras from the Category Un(Lb)

• 作者: Min Soo Kim Rustam Turdibaev
• 来源期刊: 代数集刊（英文版）
• 年，卷（期）: 2021,（1）
• 页码范围: 155-168
• 页数: 14页
• 语种: 英文
• DOI: 10.1142/S1005386721000146

摘要

We study the Leibniz n-algebra Un(∑),whose multiplication is defined viathe bracket of a Leibniz algebra ∑ as[x1,...,xn]=[x1,[...,[xn-2,[xn-1,xn]]...]].Weshow that Un(∑) is simple if and only if ∑ is a simple Lie algebra.An analog of Levi'stheorem for Leibniz algebras in Un(Lb) is established and it is proven that the Leibnizn-kernel of Un(Σ) for any semisimple Leibniz algebra Σ is the n-algebra Un(Σ).