{"paper":{"title":"Leibniz triple systems admitting a multiplicative basis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Antonio Jes\\'us Calderon, Elisabete Barreiro, Helena Albuquerque, Jos\\'e Mar\\'ia S\\'anchez-Delgado","submitted_at":"2016-06-01T10:58:23Z","abstract_excerpt":"Let $(T,\\langle \\cdot, \\cdot, \\cdot \\rangle)$ be a Leibniz triple system of arbitrary dimension, over an arbitrary base field ${\\mathbb F}$. A basis ${\\mathcal B} = \\{e_{i}\\}_{i \\in I}$ of $T$ is called multiplicative if for any $i,j,k \\in I$ we have that $\\langle e_i,e_j,e_k\\rangle\\in {\\mathbb F}e_r$ for some $r \\in I$. We show that if $T$ admits a multiplicative basis then it decomposes as the orthogonal direct sum $T= \\bigoplus_k{\\mathfrak I}_k$ of well-described ideals ${\\mathfrak I}_k$ admitting each one a multiplicative basis. Also the minimality of $T$ is characterized in terms of the m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.00217","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"}