Exotic cluster structures on $SL_{5}$
| Autor: | Idan Eisner |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2013 |
| Předmět: |
Statistics and Probability
Pure mathematics Class (set theory) Conjecture Structure (category theory) General Physics and Astronomy Lie group Statistical and Nonlinear Physics 13F60 53D17 Cluster algebra Nonlinear Sciences::Exactly Solvable and Integrable Systems Simple (abstract algebra) Modeling and Simulation Mathematics::Quantum Algebra Mathematics - Quantum Algebra Cluster (physics) FOS: Mathematics Quantum Algebra (math.QA) Representation Theory (math.RT) Mathematics::Representation Theory Mathematical Physics Mathematics - Representation Theory Mathematics |
| Popis: | A conjecture by Gekhtman, Shapiro and Vainshtein suggests a correspondence between the Belavin - Drinfeld classification of solutions of the classical Yang - Baxter equation and cluster structures on simple Lie groups. This paper confirms the conjecture for $SL_{5}$. Given a Belavin - Drinfeld class, we construct the corresponding cluster structure in $\mathcal{O}\left(SL_{5}\right)$, and show that it satisfies all parts of the conjecture. arXiv admin note: text overlap with arXiv:1101.0015 by other authors |
| Databáze: | OpenAIRE |
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