{"paper":{"title":"A characterisation of Lie algebras via algebraic exponentiation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.CT","authors_text":"Tim Van der Linden, Xabier Garc\\'ia-Mart\\'inez","submitted_at":"2017-11-02T11:28:06Z","abstract_excerpt":"In this article we describe varieties of Lie algebras via algebraic exponentiation, a concept introduced by Gray in his Ph.D. thesis. For $\\mathbb{K}$ an infinite field of characteristic different from $2$, we prove that the variety of Lie algebras over $\\mathbb{K}$ is the only variety of non-associative $\\mathbb{K}$-algebras which is a non-abelian locally algebraically cartesian closed (LACC) category. More generally, a variety of $n$-algebras $\\mathcal{V}$ is a non-abelian (LACC) category if and only if $n=2$ and $\\mathcal{V}=\\mathsf{Lie}_\\mathbb{K}$. In characteristic $2$ the situation is s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.00689","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"}