BGP-reflection functors and cluster combinatorics
| dc.creator | Zhu, Bin | |
| dc.date | 2005-11-15 | |
| dc.date | 2006-07-14 | |
| dc.date.accessioned | 2026-07-07T06:51:17Z | |
| dc.date.available | 2026-07-07T06:51:17Z | |
| dc.description | We define Bernstein-Gelfand-Ponomarev reflection functors in the cluster categories of hereditary algebras. They are triangle equivalences which provide a natural quiver realization of the "truncated simple reflections" on the set of almost positive roots $Φ_{\ge -1}$ associated to a finite dimensional semisimple Lie algebra. Combining with the tilting theory in cluster categories developed in [4], we give a unified interpretation via quiver representations for the generalized associahedra associated to the root systems of all Dynkin types (a simply-laced or non-simply-laced). This confirms the conjecture 9.1 in [4] in all Dynkin types. | |
| dc.description | version 3 | |
| dc.identifier | https://arxiv.org/abs/math/0511380 | |
| dc.identifier | http://arxiv.org/abs/math/0511380 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/104932 | |
| dc.subject | Representation Theory | |
| dc.subject | Combinatorics | |
| dc.subject | 16G20; 16G70 | |
| dc.title | BGP-reflection functors and cluster combinatorics | |
| dc.type | text |