Graphs associated with nilpotent Lie algebras of maximal rank.

Título inglés	Graphs associated with nilpotent Lie algebras of maximal rank.
Título español	Grafos asociados a álgebras de Lie nilpotentes de rango maximal.
Autor/es	Díaz, Eduardo ; Fernández-Mateos, Rafael ; Fernández-Ternero, Desamparados ; Núñez, Juan
Organización	Dep. Alg. Fac. Mat. Univ. Sevilla, Sevilla, España;Dep. Geom. Topol. Fac. Mat. Univ. Sevilla, Sevilla, España
Revista	0213-2230
Publicación	2003, 19(2): 325-338, 5 Ref.
Tipo de documento	articulo
Idioma	Inglés
Resumen inglés	In this paper, we use the graphs as a tool to study nilpotent Lie algebras. It implies to set up a link betwcen graph theory and Lie theory. To do this, it is already known that every nilpotent Lie algebra of maximal rank is associated with a generalized Cartan matrix A and it ils isomorphic to a quotient of the positive part n+ of the KacMoody algebra g(A). Then, if A is affine, we can associate n+ with a directed graph (from now on, we use the term digraph) and we can also associate a subgraph of this digraph with every isomorphism class of nilpotent Lie algebras of maximal rank and of type A. Finally, we show an algorithm which obtains these subgraphs and also groups them in isomorphism classes.
Clasificación UNESCO	120101 ; 120109
Palabras clave español	Teoría de grafos ; Algebra de Lie ; Algebra nilpotente ; Singularidades ; Geometría algebraica
Código MathReviews	MR2023187
Código Z-Math	Zbl 1055.17003
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