Non-degenerate Invariant Bilinear Forms on Leibniz Algebras

• 作者: Linsheng Zhu Song Wang
• 来源期刊: 代数集刊:英文版
• 学科: 数学
• 关键词: 莱布尼茨 双线性形式 李代数 非简并 充分条件 次对称 二阶 定理
• 年，卷（期）: 2015,（4）
• 页码范围: 711-720
• 页数: 10页
• 分类号: O172
• 语种: 中文

摘要

In this paper, we study Leibniz algebras with a non-degenerate Leibniz- symmetric fl-invariant bilinear form B, such a pair (g, B) is called a quadratic Leibniz algebra. Our first result generalizes the notion of double extensions to quadratic Leibniz algebras. This notion was introduced by Medina and Revoy to study quadratic Lie alge- bras. In the second theorem, we give a sufficient condition for a quadratic Leibniz algebra to be a quadratic Leibniz algebra by double extension.