{"paper":{"title":"On The Zariski Topology Of Automorphism Groups Of Affine Spaces And Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AC","math.AG","math.AT","math.MP"],"primary_cat":"math.RA","authors_text":"Alexei Kanel-Belov, Andrey Elishev, Jie-Tai Yu","submitted_at":"2012-07-09T13:53:22Z","abstract_excerpt":"We study the Zariski topology of the ind-groups of polynomial and free associative algebras $\\Aut(K[x_1,...,x_n])$ (which is equivalent to the automorphism group of the affine space $\\Aut(K^n))$) and $\\Aut(K< x_1,..., x_n>$ via $\\Ind$-schemes, toric varieties, approximations and singularities.\n  We obtain some nice properties of $\\Aut(\\Aut(A))$, where $A$ is polynomial or free associative algebra over a field $K$. We prove that all $\\Ind$-scheme automorphisms of $\\Aut(K[x_1,...,x_n])$ are inner for $n\\ge 3$, and all $\\Ind$-scheme automorphisms of $\\Aut(K< x_1,..., x_n>)$ are semi-inner. We als"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.2045","kind":"arxiv","version":6},"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"}