{"paper":{"title":"$n$-complete algebras and McKay quivers","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Deren Luo, Lijing Zheng, Tongliang Zhang","submitted_at":"2016-03-03T02:32:14Z","abstract_excerpt":"Let $\\Gamma^{n}$ be the cone of an $(n-1)$-complete algebra over an algebraically closed field $k$. In this paper, we prove that if the bound quiver $(Q_{n},\\rho_{n})$ of $\\Gamma^{n}$ is a truncation from the bound McKay quiver $(Q_{G},\\rho_{G})$ of a finite subgroup $G$ of $GL(n,k)$, the bound quiver $(Q_{n+1}, \\rho_{n+1})$ of $\\Gamma^{n+1}$, the cone of $\\Gamma^{n}$, is a truncation from the bound McKay quiver $(Q_{\\widetilde{G}},\\rho_{\\widetilde{G}})$ of $\\widetilde{G}$, where $\\widetilde{G}\\cong G\\times \\mathbb{Z}_{m}$ for some $m\\in \\mathbb{N}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.00949","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"}