{"paper":{"title":"Exotic Cluster Structures on $SL_n$ with Belavin-Drinfeld Data of Minimal Size, I. The Structure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Idan Eisner","submitted_at":"2014-12-17T11:53:35Z","abstract_excerpt":"Using the notion of compatibility between Poisson brackets and cluster structures in the coordinate rings of simple Lie groups, Gekhtman Shapiro and Vainshtein conjectured a correspondence between the two. 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 $SL_{n}$, we give an algorithm for constructing an initial seed $\\Sigma$ in $\\mathcal{O}(SL_{n})$. The cluster structure $\\mathcal{C}=\\mathcal{C}(\\Sigma)$ is then proved to be compatible with the Poisson bra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.5352","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}