Exotic cluster structures on SL n with Belavin–Drinfeld data of minimal size, I. The structure
| Autor: | Idan Eisner |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
0301 basic medicine
Pure mathematics Initial Seed General Mathematics Simple Lie group 010102 general mathematics Lie group 01 natural sciences 03 medical and health sciences Poisson bracket Nonlinear Sciences::Exactly Solvable and Integrable Systems 030104 developmental biology Mathematics::Quantum Algebra 0101 mathematics Mathematics::Symplectic Geometry Mathematics |
| Zdroj: | Israel Journal of Mathematics. 218:391-443 |
| ISSN: | 1565-8511 0021-2172 |
| DOI: | 10.1007/s11856-017-1469-z |
| Popis: | Using the notion of compatibility between Poisson brackets and cluster structures in the coordinate rings of simple Lie groups, Gekhtman, Shapiro and Vainshtein conjectured the existence of a cluster structure for each Belavin-Drinfeld solution of the classical Yang-Baxter equation compatible with the corresponding Poisson-Lie bracket on the simple Lie group. Poisson-Lie groups are classified by the Belavin-Drinfeld classification of solutions to the classical Yang-Baxter equation. For any non-trivial Belavin-Drinfeld data of minimal size for SLn, we give an algorithm for constructing an initial seed ∑ in O (SLn). The cluster structure C = C (∑) is then proved to be compatible with the Poisson bracket associated with that Belavin-Drinfeld data, and the seed ∑ is locally regular. |
| Databáze: | OpenAIRE |
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