Coxeter Elements and Root Bases
| dc.creator | Kirillov Jr., Alexander | |
| dc.creator | Thind, Jaimal | |
| dc.date | 2008-11-14 | |
| dc.date.accessioned | 2026-07-07T10:18:25Z | |
| dc.date.available | 2026-07-07T10:18:25Z | |
| dc.description | 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. | |
| dc.description | 13 pages, 4 figures | |
| dc.identifier | https://arxiv.org/abs/0811.2324 | |
| dc.identifier | http://arxiv.org/abs/0811.2324 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/174180 | |
| dc.subject | Representation Theory | |
| dc.subject | Combinatorics | |
| dc.title | Coxeter Elements and Root Bases | |
| dc.type | text |