{"paper":{"title":"The Automorphisms group of a Current Lie algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.RA"],"primary_cat":"math.RT","authors_text":"Jes\\'us Alonso Ochoa Arango, Nadina Elizabeth Rojas","submitted_at":"2018-11-25T05:43:50Z","abstract_excerpt":"Let $\\mathfrak{g}$ be a finite dimensional complex Lie algebra and let $A$ be a finite dimensional complex, associative and commutative algebra with unit. We describe the structure of the derivation Lie algebra of the current Lie algebra $\\mathfrak{g}_A= \\mathfrak{g} \\otimes A$, denoted by $\\operatorname{Der}(\\mathfrak{g}_A)$. Furthermore, we obtain the Levi decomposition of $\\operatorname{Der}(\\mathfrak{g}_A)$.\n  As a consequence of the last result, if $\\mathfrak{h}_m$ is the Heisenberg Lie algebra of dimension $2 m + 1$, we obtain a faithful representation of $\\operatorname{Der}(\\mathfrak{h}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.09948","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"}