An obstruction to represent abelian Lie Algebras by unipotent matrices

1. Echarte Reula, Francisco Javier
2. Núñez-Valdés, Juan
3. Tenorio Villalón, Ángel Francisco
4. Benjumea, J.C.

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Abstract

The aim of this paper is the study of abelian Lie algebras as subalgebras of the nilpotent Lie algebra gn associated with Lie groups of upper-triangular square matrices whose main diagonal is formed by 1. We also give an obstruction to obtain the abelian Lie algebra of dimension one unit less than the corresponding to gn as a Lie subalgebra of gn. Moreover, we give a procedure to obtain abelian Lie subalgebras of gn up to the dimension which we think it is the maximum.

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