{"paper":{"title":"Decompositions of the automorphism group of a locally compact abelian group","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.CT","math.GR"],"primary_cat":"math.GN","authors_text":"Iian B. Smythe","submitted_at":"2011-10-10T04:32:07Z","abstract_excerpt":"It is well known that every locally compact abelian group L can be decomposed as L_1 \\oplus R^n, where L_1 contains a compact-open subgroup. In this paper, we use this decomposition to study the topological group Aut(L) of automorphisms of L, equipped with the g-topology. We show that Aut(L) is topologically isomorphic to a matrix group with entries from Aut(L_1), Hom(L_1, R^n), Hom(R^n, L_1), and GL_n(R), respectively. It is also shown that the algebraic portion of the decomposition is not specific to locally compact abelian groups, but is also true for objects with a well-behaved decompositi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.1923","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"}