Cluster algebras III: Upper bounds and double Bruhat cells
| dc.creator | Berenstein, Arkady | |
| dc.creator | Fomin, Sergey | |
| dc.creator | Zelevinsky, Andrei | |
| dc.date | 2003-05-30 | |
| dc.date | 2004-01-21 | |
| dc.date.accessioned | 2026-07-07T04:58:24Z | |
| dc.date.available | 2026-07-07T04:58:24Z | |
| dc.description | We continue the study of cluster algebras initiated in math.RT/0104151 and math.RA/0208229. We develop a new approach based on the notion of an upper cluster algebra, defined as an intersection of certain Laurent polynomial rings. Strengthening the Laurent phenomenon from math.RT/0104151, we show that, under an assumption of "acyclicity", a cluster algebra coincides with its "upper" counterpart, and is finitely generated. In this case, we also describe its defining ideal, and construct a standard monomial basis. We prove that the coordinate ring of any double Bruhat cell in a semisimple complex Lie group is naturally isomorphic to the upper cluster algebra explicitly defined in terms of relevant combinatorial data. | |
| dc.description | 39 pages. Minor editorial changes, a reference added. This is the final version, to appear in Duke Mathematical Journal | |
| dc.identifier | https://arxiv.org/abs/math/0305434 | |
| dc.identifier | http://arxiv.org/abs/math/0305434 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67621 | |
| dc.subject | Representation Theory | |
| dc.subject | Commutative Algebra | |
| dc.subject | Algebraic Geometry | |
| dc.title | Cluster algebras III: Upper bounds and double Bruhat cells | |
| dc.type | text |