, Volume 152, Issue 3, pp 1225-1233

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

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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.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 152, No. 3, pp. 419–429, September, 2007.