Cluster algebras III: Upper bounds and double Bruhat cells
Abstrak
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.
Topik & Kata Kunci
Penulis (3)
A. Berenstein
S. Fomin
A. Zelevinsky
Akses Cepat
- Tahun Terbit
- 2003
- Bahasa
- en
- Total Sitasi
- 697×
- Sumber Database
- Semantic Scholar
- DOI
- 10.1215/S0012-7094-04-12611-9
- Akses
- Open Access ✓