{"paper":{"title":"Finitistic dimensions and piecewise hereditary property of skew group algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"Liping Li","submitted_at":"2013-04-01T21:09:16Z","abstract_excerpt":"Let $\\Lambda$ be a finite dimensional algebra and $G$ be a finite group whose elements act on $\\Lambda$ as algebra automorphisms. Under the assumption that $\\Lambda$ has a complete set $E$ of primitive orthogonal idempotents, closed under the action of a Sylow $p$-subgroup $S \\leqslant G$. If the action of $S$ on $E$ is free, we show that the skew group algebra $\\Lambda G$ and $\\Lambda$ have the same finitistic dimension, and have the same strong global dimension if the fixed algebra $\\Lambda^S$ is a direct summand of the $\\Lambda^S$-bimodule $\\Lambda$. Using a homological characterization of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0482","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"}