Maximal Abelian Dimensions in Some Families of Nilpotent Lie Algebras

被引：5

作者：

Benjumea, Juan C. ^{[2
]}

Nunez, Juan ^{[2
]}

Tenorio, Angel F. ^{[1
]}

机构：

[1] Univ Pablo Olavide, Dept Econ Metodos Cuantitat & Ha Econ, Escuela Politecn Super, Seville 41013, Spain

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

来源：

ALGEBRAS AND REPRESENTATION THEORY | 2012年 / 15卷 / 04期

关键词：

Nilpotent Lie algebras; Maximal abelian dimension; Heisenberg algebras; BLACK-HOLES;

D O I：

10.1007/s10468-010-9260-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper deals with the maximal abelian dimension of a Lie algebra, that is, the maximal value for the dimensions of its abelian Lie subalgebras. Indeed, we compute the maximal abelian dimension for every nilpotent Lie algebra of dimension less than 7 and for the Heisenberg algebra , with . In this way, an algorithmic procedure is introduced and applied to compute the maximal abelian dimension for any arbitrary nilpotent Lie algebra with an arbitrary dimension. The maximal abelian dimension is also given for some general families of nilpotent Lie algebras.

引用

页码：697 / 713

页数：17

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