{"paper":{"title":"Finite-dimensional representations of minimal nilpotent W-algebras and zigzag algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"Alexey Petukhov","submitted_at":"2016-10-11T17:00:26Z","abstract_excerpt":"Let $\\frak g$ be a simple finite-dimensional Lie algebra over an algebraically closed field $\\mathbb F$ of characteristic 0. We denote by $\\operatorname{U}(\\frak g)$ the universal enveloping algebra of $\\frak g$. To any nilpotent element $e\\in \\frak g$ one can attach an associative (and noncommutative as a general rule) algebra $\\operatorname{U}({\\frak g},~e)$ which is in a proper sense a \"tensor factor\" of $\\operatorname{U}(\\frak g)$. In this article we consider the case in which $\\frak g$ is simple and $e$ belongs of the minimal nonzero nilpotent orbit of $\\frak g$. Under these assumptions $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.03423","kind":"arxiv","version":2},"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"}