{"paper":{"title":"Classical Yang-Baxter equations and Nijenhuis operators for Lie algebras","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Haiying Li, Tianshui Ma","submitted_at":"2025-02-26T00:21:41Z","abstract_excerpt":"In this paper the conditions that when a Lie algebra is Nijenhuis are investigated. Furthermore all the Nijenhuis operators on $\\mathfrak{sl}_2$ under the standard Cartan-Weyl basis are given. On the other hand, the relations between the classical Yang-Baxter equation and Nijenhuis operators $N$ on a Lie algebra and $P$ on a Lie coalgebra are derived by means of the bialgebraic theory for Nijenhuis Lie algebras."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.18717","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.18717/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}