Algorithmic procedure to compute abelian subalgebras and ideals of maximal dimension of Leibniz algebras

被引：3

作者：

Ceballos, Manuel ^{[1
]}

Nunez, Juan ^{[1
]}

Tenorio, Angel F. ^{[2
]}

机构：

[1] Univ Seville, Fac Matemat, Dept Geometria & Topol, E-41080 Seville, Spain

[2] Univ Pablo de Olavide, Escuela Politecn Super, Dept Econ Metodos Cuantitat & Hist Econ, Seville 41013, Sevilla, Spain

来源：

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS | 2015年 / 92卷 / 09期

关键词：

beta invariant; Leibniz algebra; abelian ideal; algorithm; abelian subalgebra; alpha invariant; 68Q25; 17A60; 17-08; 17A32; 68W30; CLASSIFICATION;

D O I：

10.1080/00207160.2014.884216

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we show an algorithmic procedure to compute abelian subalgebras and ideals of a given finite-dimensional Leibniz algebra, starting from the non-zero brackets in its law. In order to implement this method, the symbolic computation package MAPLE 12 is used. Moreover, we also show a brief computational study considering both the computing time and the memory used in the two main routines of the implementation. Finally, we determine the maximal dimension of abelian subalgebras and ideals for 3-dimensional Leibniz algebras and 4-dimensional solvable ones over .

引用

页码：1838 / 1854

页数：17

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