The maximal Abelian dimension of linear algebras formed by strictly upper triangular matrices期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

The maximal Abelian dimension of linear algebras formed by strictly upper triangular matrices

Authors:	J. C. Benjumea J. Núñez Á. F. Tenorio

Affiliation:	(1) Departamento de Geometría y Topología, Facultad de Matemáticas, Universidad de Sevilla, Spain;(2) Departamento de Economía, Métodos Cuantitativos e Ha Económica, Escuela Politécnica Superior, Universidad Pablo de Olavide, Spain

Abstract:	We compute the largest dimension of the Abelian Lie subalgebras contained in the Lie algebra $mathfrak{g}_n$ of n×n strictly upper triangular matrices, where n ∈ ℕ {1}. We do this by proving a conjecture, which we previously advanced, about this dimension. We introduce an algorithm and use it first to study the two simplest particular cases and then to study the general case. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 152, No. 3, pp. 419–429, September, 2007.

Keywords:	nilpotent Lie algebra maximal Abelian dimension strictly upper triangular matrix
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