{"paper":{"title":"Reductivity of the Lie algebra of a bilinear form","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Fernando Szechtman, Martin Chaktoura, S. Ruhallah Ahmadi","submitted_at":"2013-08-21T15:43:09Z","abstract_excerpt":"Let $f:V\\times V\\to F$ be a totally arbitrary bilinear form defined on a finite dimensional vector space $V$ over a a field $F$, and let $L(f)$ be the subalgebra of $\\gl(V)$ of all skew-adjoint endomorphisms relative to $f$. Provided $F$ is algebraically closed of characteristic not 2, we determine all $f$, up to equivalence, such that $L(f)$ is reductive. As a consequence, we find, over an arbitrary field, necessary and sufficient conditions for $L(f)$ to be simple, semisimple or isomorphic to $\\sl(n)$ for some $n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.4617","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"}