Non-degenerate Invariant Bilinear Forms on Leibniz Algebras  

作　　者：Song Wang Linsheng Zhu 

机构地区：[1]Department of Mathematics, Tngji University, Shanghai 200092, China College of Information Technology, Shanghai Ocean University Shanghai 201306, China [2]Department of Mathematics, Changshu Institute of Technology Changshu, Jiangsu 215500, China

出　　处：《Algebra Colloquium》2015年第4期711-720,共10页代数集刊（英文版）

基　　金：Supported by the National Natural Science Foundation of China （10571119, 10671027, 11271056, 11271284）, the Foundation of Jiangsu Educational Committee, the Fundamental Research Funds for the Central Universities and the Youth Scholars of Shanghai Higher Education Institutions （Gr~nt No.ZZHY14026）.

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.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.

关 键 词：quadratic Leibniz algebra double extension 

分 类 号：O172[理学—数学] O411.1[理学—基础数学]