{"paper":{"title":"Bialgebras induced by special left Alia algebras","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Chan Zhao, Huihui Zheng, Tianshui Ma","submitted_at":"2025-06-08T09:44:25Z","abstract_excerpt":"Special left Alia algebras were introduced by Dzhumadil'daev in [J. Math. Sci. (N.Y.) 161(2009), 11-30] when studying the classification of algebras with skew-symmetric identity of degree 3. A special left Alia algebra (resp. coalgebra) $(A, [,]_{(f,g)})$ (resp. $(A, \\Delta_{(F,G)})$) is constructed by a commutative associative algebra (resp. cocommutative coassociative coalgebra) $(A, \\cdot)$ (resp. $(A, \\delta)$) together with two linear maps $f, g: A\\longrightarrow A$ (resp. $F, G: A\\longrightarrow A$). We find that if $((A, \\cdot), f)$ (resp. $((A, \\delta), F)$) is a Nijenhuis associative "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.07061","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.07061/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"}