{"paper":{"title":"$\\tau$-slice algebras of $n$-translation algebras and quasi $n$-Fano algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"Cong Xiao, Jin Yun Guo","submitted_at":"2017-07-05T13:51:36Z","abstract_excerpt":"In this paper, we show that the $n$-APR tilts of dual $\\tau$-slice algebras of acyclic stable $n$-translation algebras are realized as $\\tau$-mutations. Such dual $\\tau$-slice algebras are quasi $(n-1)$-Fano when the $n$-translation algebra is Koszul, and a recursive construction of higher quasi Fano algebras for quasi $n$-Fano algebra obtained in this way is given. The $\\tau_n$-closure and $\\nu_n$-closure of such algebras are studied and we show that for an acyclic dual $n$-translation algebras with bound quiver $Q^{\\perp}$, the Auslander-Reiten quivers of its $\\tau_n$-closures are truncation"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.01393","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"}