{"paper":{"title":"Generalized McKay Quivers, Root System and Kac-Moody Algebras","license":"http://creativecommons.org/licenses/publicdomain/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"Bo Hou, Shilin Yang","submitted_at":"2011-02-19T02:12:36Z","abstract_excerpt":"Let $Q$ be a finite quiver and $G\\subseteq\\Aut(\\mathbbm{k}Q)$ a finite abelian group. Assume that $\\hat{Q}$ and $\\Gamma$ is the generalized Mckay quiver and the valued graph corresponding to $(Q, G)$ respectively. In this paper we discuss the relationship between indecomposable $\\hat{Q}$-representations and the root system of Kac-Moody algebra $\\mathfrak{g}(\\Gamma)$. Moreover, we may lift $G$ to $\\bar{G}\\subseteq\\Aut(\\mathfrak{g}(\\hat{Q}))$ such that $\\mathfrak{g}(\\Gamma)$ embeds into the fixed point algebra $\\mathfrak{g}(\\hat{Q})^{\\bar{G}}$ and $\\mathfrak{g}(\\hat{Q})^{\\bar{G}}$ as $\\mathfrak{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.3951","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"}