{"paper":{"title":"Free algebras arising from positive-entropy automorphisms of surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"S. Paul Smith","submitted_at":"2013-08-18T22:50:57Z","abstract_excerpt":"Let X be a smooth projective surface defined over an uncountable algebraically closed field k and let k(X) be its field of rational functions. Let s be an automorphism of X. This paper proves there is a non-negative integer n and elements a and b in k(X) such that the subalgebra of the skew Laurent extension k(X)[t, t^{-1};s] generated by at^n and bt^n is a free algebra if and only if the spectral radius for the action of s^* on the Neron-Severi group of X is >1. Thus, when s is an automorphism of a smooth complex projective surface X, C(X)[t,t^{-1};s] has a free subalgebra on >1 variables if "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.3902","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"}