Coxeter Elements and Periodic Auslander-Reiten Quiver
| dc.creator | Kirillov Jr., Alexander | |
| dc.creator | Thind, Jaimal | |
| dc.date | 2007-03-12 | |
| dc.date | 2007-05-25 | |
| dc.date.accessioned | 2026-07-07T08:03:10Z | |
| dc.date.available | 2026-07-07T08:03:10Z | |
| dc.description | In this paper we show that for a simply-laced root system a choice of $C$ gives rise to a natural construction of the Dynkin diagram, in which vertices of the diagram correspond to $C$-orbits in $R$; moreover, it gives an identification of $R$ with a certain subset $Ihat$ of $I x Z_{2h}$, where $h$ is the Coxeter number. The set $Ihat$ has a natural quiver structure; we call it the periodic Auslander-Reiten quiver. This gives a combinatorial construction of the root system associated with the Dynkin diagram $I$: roots are vertices of $Ihat$, and the root lattice and the inner product admit an explicit description in terms of $Ihat$. Finally, we relate this construction to the theory of quiver representations. | |
| dc.description | 27 pages, 10 figures. v2: Added new sections relating our results to the theory of quiver representations | |
| dc.identifier | https://arxiv.org/abs/math/0703361 | |
| dc.identifier | http://arxiv.org/abs/math/0703361 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/129479 | |
| dc.subject | Representation Theory | |
| dc.subject | Combinatorics | |
| dc.title | Coxeter Elements and Periodic Auslander-Reiten Quiver | |
| dc.type | text |