Coxeter Elements and Root Bases

dc.creatorKirillov Jr., Alexander
dc.creatorThind, Jaimal
dc.date2008-11-14
dc.date.accessioned2026-07-07T10:18:25Z
dc.date.available2026-07-07T10:18:25Z
dc.descriptionLet 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.
dc.description13 pages, 4 figures
dc.identifierhttps://arxiv.org/abs/0811.2324
dc.identifierhttp://arxiv.org/abs/0811.2324
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/174180
dc.subjectRepresentation Theory
dc.subjectCombinatorics
dc.titleCoxeter Elements and Root Bases
dc.typetext

Files

Collections