Minimal linear representations of the low-dimensional nilpotent Lie algebras
- J.C. Benjumea
- Juan Núñez Valdés
- Ángel Francisco Tenorio
ISSN: 0025-5521
Année de publication: 2008
Volumen: 102
Número: 1
Pages: 17-26
Type: Article
D'autres publications dans: Mathematica scandinavica
Résumé
The main goal of this paper is to compute a minimal matrix representation for each non-isomorphic nilpotent Lie algebra of dimension less than 6. Indeed, for each of these algebras, we search the natural number n∈N∖{1} such that the linear algebra gn, formed by all the n×n complex strictly upper-triangular matrices, contains a representation of this algebra. Besides, we show an algorithmic procedure which computes such a minimal representation by using the Lie algebras gn. In this way, a classification of such algebras according to the dimension of their minimal matrix representations is obtained. In this way, we improve some results by Burde related to the value of the minimal dimension of the matrix representations for nilpotent Lie algebras.