Geodesic
The~maximal Abelian dimension of linear algebras formed by strictly upper triangular matrices
Teoretičeskaâ i matematičeskaâ fizika, Tome 152 (2007) no. 3, pp. 419-429

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We compute the largest dimension of the Abelian Lie subalgebras contained in the Lie algebra $\mathfrak g_n$ of $n\times n$ strictly upper triangular matrices, where $n\in\mathbb N\setminus\{1\}$. 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.
Keywords: nilpotent Lie algebra, strictly upper triangular matrix.
Mots-clés : maximal Abelian dimension 
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     author = {J. C. Benjumea and J. Nunez and A. F. Tenorio},
     title = {The~maximal {Abelian} dimension of linear algebras formed by strictly upper triangular matrices},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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J. C. Benjumea; J. Nunez; A. F. Tenorio. The~maximal Abelian dimension of linear algebras formed by strictly upper triangular matrices. Teoretičeskaâ i matematičeskaâ fizika, Tome 152 (2007) no. 3, pp. 419-429. http://geodesic.mathdoc.fr/item/TMF_2007_152_3_a0/