{"paper":{"title":"$m$-cluster tilted algebras of euclidean type","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"Ana Garcia Elsener, Elsa Fern\\'andez, Sonia Trepode","submitted_at":"2018-01-15T20:28:29Z","abstract_excerpt":"We consider $m$-cluster tilted algebras arising from quivers of Euclidean type and we give necessary and sufficient conditions for those algebras to be representation finite. For the case $\\widetilde{A}$, using the geometric realization, we get a description of representation finite type in terms of $(m+2)$-angulations. We establish which $m$-cluster tilted algebras arise at the same time from quivers of type $A$ and $\\widetilde{A}$. Finally, we characterize representation infinite $m$-cluster tilted algebras arising from a quiver of type $\\widetilde{A}$ as $m$-relations extensions of some ite"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.04989","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"}