{"paper":{"title":"On the existence of an invariant non-degenerate bilinear form under a linear map","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Krishnendu Gongopadhyay, Ravi S. Kulkarni","submitted_at":"2009-03-04T17:50:05Z","abstract_excerpt":"Let $\\V$ be a vector space over a field $\\F$. Assume that the characteristic of $\\F$ is \\emph{large}, i.e. $char(\\F)>\\dim \\V$. Let $T: \\V \\to \\V$ be an invertible linear map. We answer the following question in this paper: When does $\\V$ admit a $T$-invariant non-degenerate symmetric (resp. skew-symmetric) bilinear form? We also answer the infinitesimal version of this question.\n  Following Feit-Zuckerman \\cite{fz}, an element $g$ in a group $G$ is called real if it is conjugate in $G$ to its own inverse. So it is important to characterize real elements in $\\G(\\V, \\F)$. As a consequence of the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.0826","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"}