Classification of Some Solvable Leibniz Algebras

被引：7

作者：

Demir, Ismail ^{[1
]}

Misra, Kailash C. ^{[1
]}

Stitzinger, Ernie ^{[1
]}

机构：

[1] N Carolina State Univ, Dept Math, Box 8205, Raleigh, NC 27695 USA

来源：

ALGEBRAS AND REPRESENTATION THEORY | 2016年 / 19卷 / 02期

关键词：

Leibniz algebra; Solvability; Nilpotency; Classification;

D O I：

10.1007/s10468-015-9580-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Leibniz algebras are certain generalization of Lie algebras. In this paper we give classification of non-Lie solvable (left) Leibniz algebras of dimension <= 8 with one dimensional derived subalgebra. We use the canonical forms for the congruence classes of matrices of bilinear forms to obtain our result. Our approach can easily be extended to classify these algebras of higher dimensions. We also revisit the classification of three dimensional non-Lie solvable (left) Leibniz algebras.

引用

页码：405 / 417

页数：13

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