{"paper":{"title":"On the invariant theory for tame tilted algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Calin Chindris","submitted_at":"2011-09-13T20:26:20Z","abstract_excerpt":"We show that a tilted algebra $A$ is tame if and only if for each generic root $\\dd$ of $A$ and each indecomposable irreducible component $C$ of $\\module(A,\\dd)$, the field of rational invariants $k(C)^{\\GL(\\dd)}$ is isomorphic to $k$ or $k(x)$. Next, we show that the tame tilted algebras are precisely those tilted algebras $A$ with the property that for each generic root $\\dd$ of $A$ and each indecomposable irreducible component $C \\subseteq \\module(A,\\dd)$, the moduli space $\\M(C)^{ss}_{\\theta}$ is either a point or just $\\mathbb P^1$ whenever $\\theta$ is an integral weight for which $C^s_{\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.2915","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"}