Abstract
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.
Citation
Eduardo Díaz. Rafael Fernández-Mateos. Desamparados Fernández-Ternero. Juan Núñez. "Graphs associated with nilpotent Lie algebras of maximal rank." Rev. Mat. Iberoamericana 19 (2) 325 - 338, September, 2003.
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