{"paper":{"title":"Ergodicity of principal algebraic group actions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Hanfeng Li, Jesse Peterson, Klaus Schmidt","submitted_at":"2013-12-11T09:51:42Z","abstract_excerpt":"An \\textit{algebraic} action of a discrete group $\\Gamma $ is a homomorphism from $\\Gamma $ to the group of continuous automorphisms of a compact abelian group $X$. By duality, such an action of $\\Gamma $ is determined by a module $M=\\widehat{X}$ over the integer group ring $\\mathbb{Z}\\Gamma $ of $\\Gamma $. The simplest examples of such modules are of the form $M=\\mathbb{Z}\\Gamma /\\mathbb{Z}\\Gamma f$ with $f\\in \\mathbb{Z}\\Gamma $; the corresponding algebraic action is the \\textit{principal algebraic $\\Gamma $-action} $\\alpha _f$ defined by $f$.\n  In this note we prove the following extensions "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.3098","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"}