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


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.


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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.


Published: September, 2003
First available in Project Euclid: 8 September 2003

zbMATH: 1055.17003
MathSciNet: MR2023187

Primary: 05C20‎ , 05C85 , 14B05 , 17B30 , 17B65 , 32S20 , 32S45

Keywords: Directed graph , Kac-Moody algebra , maximal rank , nilpotent

Rights: Copyright © 2003 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.19 • No. 2 • September, 2003
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