, Volume 152, Issue 3, pp 1225-1233

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

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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.