{"paper":{"title":"Cluster algebra structures and semicanonical bases for unipotent groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"Bernard Leclerc, Christof Geiss, Jan Schr\\\"oer","submitted_at":"2007-03-01T17:35:26Z","abstract_excerpt":"Let Q be a finite quiver without oriented cycles, and let $\\Lambda$ be the associated preprojective algebra. To each terminal representation M of Q (these are certain preinjective representations), we attach a natural subcategory $C_M$ of $mod(\\Lambda)$. We show that $C_M$ is a Frobenius category,and that its stable category is a Calabi-Yau category of dimension 2. Then we develop a theory of mutations of maximal rigid objects of $C_M$, analogous to the mutations of clusters in Fomin and Zelevinsky's theory of cluster algebras. We show that $C_M$ yields a categorification of a cluster algebra "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0703039","kind":"arxiv","version":4},"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"}