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 and it is isomorphic to a quotient of the positive part of the Kac-Moody algebra . Then, if is affine, we can associate 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 . Finally, we show an algorithm which obtains these subgraphs and also groups them in isomorphism classes.
Cite this article
Eduardo Diáz, Rafael Fernández-Mateos, Desemparados Fernández-Ternero, Juan Núñez, Graphs associated with nilpotent Lie algebras of maximal rank. Rev. Mat. Iberoam. 19 (2003), no. 2, pp. 325–338DOI 10.4171/RMI/349