{"paper":{"title":"On standard derived equivalences of orbit categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.RT","authors_text":"Alexandra Zvonareva, Yury Volkov","submitted_at":"2015-01-04T19:29:29Z","abstract_excerpt":"Let $\\kk$ be a commutative ring, $\\AAA$ and $\\BB$ -- two $\\kk$-linear categories with an action of a group $G$. We introduce the notion of a standard $G$-equivalence from $\\Kb\\BB$ to $\\Kb\\AAA$. We construct a map from the set of standard $G$-equivalences to the set of standard equivalences from $\\Kb\\BB$ to $\\Kb\\AAA$ and a map from the set of standard $G$-equivalences from $\\Kb\\BB$ to $\\Kb\\AAA$ to the set of standard equivalences from $\\Kb(\\BB/G)$ to $\\Kb(\\AAA/G)$. We investigate the properties of these maps and apply our results to the case where $\\AAA=\\BB=R$ is a Frobenius $\\kk$-algebra and $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.00709","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"}