{"paper":{"title":"Inductions and restrictions for stable equivalences of Morita type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"Changchang Xi, Hongxing Chen, Shengyong Pan","submitted_at":"2010-12-10T03:44:41Z","abstract_excerpt":"In this paper, we present two methods, induction and restriction procedures, to construct new stable equivalences of Morita type. Suppose that a stable equivalence of Morita type between two algebras $A$ and $B$ is defined by a $B$-$A$-bimodule $N$. Then, for any finite admissible set $\\Phi$ and any generator $X$ of the $A$-module category, the $\\Phi$-Auslander-Yoneda algebras of $X$ and $N\\otimes_AX$ are stably equivalent of Morita type. Moreover, under certain conditions, we transfer stable equivalences of Morita type between $A$ and $B$ to ones between $eAe$ and $fBf$, where $e$ and $f$ are"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.2170","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"}