Theoretical and Mathematical Physics

, Volume 152, Issue 3, pp 1225–1233

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


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


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.


nilpotent Lie algebramaximal Abelian dimensionstrictly upper triangular matrix

Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  1. 1.Departamento de Geometría y Topología, Facultad de MatemáticasUniversidad de SevillaSpain
  2. 2.Departamento de Economía, Métodos Cuantitativos e Ha Económica, Escuela Politécnica SuperiorUniversidad Pablo de OlavideSpain