{"paper":{"title":"On the Conjugacy Classes in the orthogonal and symplectic groups over algebraically closed fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.GR","authors_text":"Krishnendu Gongopadhyay","submitted_at":"2009-11-02T18:20:28Z","abstract_excerpt":"Let $\\F$ be an algebraically closed field. Let $\\V$ be a vector space equipped with a non-degenerate symmetric or symplectic bilinear form $B$ over $\\F$. Suppose the characteristic of $\\F$ is \\emph{large}, i.e. either zero or greater than the dimension of $\\V$. Let $I(\\V, B)$ denote the group of isometries. Using the Jacobson-Morozov lemma we give a new and simple proof of the fact that two elements in $I(\\V,B)$ are conjugate if and only if they have the same elementary divisors."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.0379","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"}