{"paper":{"title":"On the Tits-Kantor-Koecher construction of unital Jordan bimodules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Iryna Kashuba, Vera Serganova","submitted_at":"2015-02-26T00:29:04Z","abstract_excerpt":"In this paper we explore relationship between representations of a Jordan algebra $\\J$ and the Lie algebra $\\g$ obtained from $\\J$ by the Tits-Kantor-Koecher construction. More precisely, we construct two adjoint functors $Lie :\\JJ\\to \\ggm$ and $Jor:\\ggm\\to\\JJ$, where $\\JJ$ is the category of unital $\\J$-bimodules and $\\ggm$ is the category of $\\g$-modules admitting a short grading. Using these functors we classify $\\J$ such that its semisimple part is of Clifford type and the category $\\JJ$ is tame."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.07407","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"}