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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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Authors and Affiliations

  1. Departamento de Geometría y Topología, Facultad de Matemáticas, Universidad de Sevilla, Spain

    J. C. Benjumea & J. Núñez

  2. Departamento de Economía, Métodos Cuantitativos e Ha Económica, Escuela Politécnica Superior, Universidad Pablo de Olavide, Spain

    Á. F. Tenorio

Authors
  1. J. C. Benjumea
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  2. J. Núñez
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  3. Á. F. Tenorio
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Corresponding author

Correspondence to J. C. Benjumea.

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

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Benjumea, J.C., Núñez, J. & Tenorio, Á.F. The maximal Abelian dimension of linear algebras formed by strictly upper triangular matrices. Theor Math Phys 152, 1225–1233 (2007). https://doi.org/10.1007/s11232-007-0107-z

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  • DOI: https://doi.org/10.1007/s11232-007-0107-z

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