{"paper":{"title":"Quivers with relations arising from Koszul algebras of $\\mathfrak g$-invariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"Jacob Greenstein","submitted_at":"2008-10-08T20:21:35Z","abstract_excerpt":"Let $\\mathfrak g$ be a complex simple Lie algebra and let $\\Psi$ be an extremal set of positive roots. One associates with $\\Psi$ an infinite dimensional Koszul algebra $\\bold S_\\Psi^{\\lie g}$ which is a graded subalgebra of the locally finite part of $((\\bold V)^{op}\\tensor S(\\lie g))^{\\lie g}$, where $\\bold V$ is the direct sum of all simple finite dimensional $\\lie g$-modules. We describe the structure of the algebra $\\bold S_\\Psi^{\\lie g}$ explicitly in terms of an infinite quiver with relations for $\\lie g$ of types $A$ and $C$. We also describe several infinite families of quivers and fi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0810.1532","kind":"arxiv","version":1},"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"}