Theoretical and Mathematical Physics

, Volume 152, Issue 3, pp 1225–1233

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

Authors

    • Departamento de Geometría y Topología, Facultad de MatemáticasUniversidad de Sevilla
  • J. Núñez
    • Departamento de Geometría y Topología, Facultad de MatemáticasUniversidad de Sevilla
  • Á. F. Tenorio
    • Departamento de Economía, Métodos Cuantitativos e Ha Económica, Escuela Politécnica SuperiorUniversidad Pablo de Olavide
Article

DOI: 10.1007/s11232-007-0107-z

Cite this article as:
Benjumea, J.C., Núñez, J. & Tenorio, Á.F. Theor Math Phys (2007) 152: 1225. doi:10.1007/s11232-007-0107-z

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.

Keywords

nilpotent Lie algebramaximal Abelian dimensionstrictly upper triangular matrix
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Copyright information

© Springer Science+Business Media, Inc. 2007