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Minimal linear representations of the low-dimensional nilpotent lie algebras


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Opened Access Minimal linear representations of the low-dimensional nilpotent lie algebras
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Author: Benjumea Acevedo, Juan Carlos
Núñez Valdés, Juan
Tenorio Villalón, Ángel Francisco
Department: Universidad de Sevilla. Departamento de Geometría y Topología
Date: 2008
Published in: Mathematica scandinavica, 102(1), 17–26
Document type: Article
Abstract: 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 n, 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 n. 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.
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