{"paper":{"title":"Groebner-Shirshov basis of the universal enveloping Rota-Baxter algebra of a Lie algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Pavel Kolesnikov, Vsevolod Gubarev","submitted_at":"2016-02-24T06:20:45Z","abstract_excerpt":"Consider the class RBLie of Lie algebras equipped with a Rota---Baxter operator. Then the forgetful functor RBLie --> Lie has a left adjoint one denoted by $U_{RB}(\\cdot)$. We prove an \"operator\" analogue of the Poincare---Birkhoff---Witt theorem for $U_{RB}(L)$, where $L$ is an arbitrary Lie algebra, by means of Gr\\\"obner---Shirshov bases theory for Lie algebras with an additional operator."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.07409","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"}