On the Structure of Graded Leibniz Algebras

• 作者: Antonio J. Calderon Martin Jose M. Sfinchez Delgado
• 来源期刊: 代数集刊:英文版
• 学科: 数学
• 关键词: 代数 结构 莱布尼兹 组成部分 子空间 位元件 基域 中相
• 年，卷（期）: 2015,（1）
• 页码范围: 83-96
• 页数: 14页
• 分类号: O172
• 语种: 中文

摘要

We study the structure of graded Leibniz algebras with arbitrary dimension and over an arbitrary base field K. We show that any of such algebras ￡ with a symmetric G-support is of the form ￡ = U-∑jIj with U a subspace of ￡1, the homogeneous component associated to the unit element 1 in G, and any Ij a well described graded ideal of ￡, satisfying [Ij, Ik]= 0 if j≠ k. In the case of ￡ being of maximal length, we characterize the gr-simplicity of the algebra in terms of connections in the support of the grading.