{"paper":{"title":"Automorphisms of the semigroup of endomorphisms of free associative algebras","license":"","headline":"","cross_cats":["math.AC"],"primary_cat":"math.RA","authors_text":"A. Berzins, A. Kanel-Belov, R. Lipyanski","submitted_at":"2005-12-13T14:26:16Z","abstract_excerpt":"Let $A=A(x_{1},...,x_{n})$ be a free associative algebra in $\\mathcal{A}$ freely generated over $K$ by a set $X=\\{x_{1},...,x_{n}\\}$, $End A$ be the semigroup of endomorphisms of $A$, and $Aut End A$ be the group of automorphisms of the semigroup $End A$. We investigate the structure of the groups $Aut End A$ and $Aut \\mathcal{A}^{\\circ}$, where $\\mathcal{A}^{\\circ}$ is the category of finitely generated free algebras from $\\mathcal{A}$. We prove that the group $Aut End A$ is generated by semi-inner and mirror automorphisms of $End F$ and the group $Aut \\mathcal{A}^{\\circ}$ is generated by sem"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0512273","kind":"arxiv","version":3},"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"}