Graphs associated with nilpotent Lie algebras of maximal rank
- Autores: José Eduardo Díaz Delgado, R. Fernández Mateos, Desamparados Fernández Ternero, Juan Núñez-Valdés
- Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 19, Nº 2, 2003, págs. 325-338
- Idioma: inglés
- Enlaces
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Resumen
In this paper, we use the graphs as a tool to study nilpotent Lie algebras. It implies to set up a link between 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 is isomorphic to a quotient of the positive part $\mathfrak{n}_+$ of the Kac-Moody algebra $\mathfrak{g}(A)$. Then, if $A$ is affine, we can associate $\mathfrak{n}_+$ 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.
