Coxeter Elements and Root Bases

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Let g be a Lie algebra of type A,D,E with fixed Cartan subalgebra h, root system R and Weyl group W. We show that a choice of Coxeter element C gives a root basis for g. Moreover we show that this root basis gives a purely combinatorial construction of g, where root vectors correspond to vertices of a certain quiver $Gammahat$, and show that with respect to this basis the structure constants of the Lie bracket are given by paths in $Gammahat$. This construction is then related to the constructions of Ringel and Peng and Xiao.
13 pages, 4 figures

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Representation Theory, Combinatorics

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http://salesiana.dossiersoluciones.com/handle/123456789/174180

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0811.2324
 http://arxiv.org/abs/0811.2324

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arXiv