{"paper":{"title":"Coefficients of \\v{S}apovalov elements for simple Lie algebras and contragredient Lie superalgebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Ian M. Musson","submitted_at":"2013-11-04T03:04:56Z","abstract_excerpt":"We provide upper bounds on the degrees of the coefficients of \\v{S}apovalov elements for a simple Lie algebra. If $\\fg$ is a contragredient Lie superalgebra and $\\gc$ is a positive isotropic root of $\\fg,$ we prove the existence and uniqueness of the \\v{S}apovalov element for $\\gc$ and we obtain upper bounds on the degrees of their coefficients. For type A Lie superalgebras we give a closed formula for \\v{S}apovalov elements.\n  Often the coefficients of \\v{S}apovalov elements are products of linear factors, and we provide some reasons for this coming from representation theory. We also explore"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.0570","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"}