{"paper":{"title":"Twisted Rota-Baxter family operators on Hom-associative algebras","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Wen Teng, Yunpeng Xiao","submitted_at":"2024-10-26T13:12:26Z","abstract_excerpt":"In this paper, we first define twisted Rota-Baxter family operators on Hom-associative algebras indexed by a semigroup $\\Omega$. Then we introduce and study Hom-NS-family algebras as the underlying structures of twisted Rota-Baxter family operators. Meanwhile, We show that a Hom-NS-family algebra induces an ordinary Hom-NS-algebra on the tensor product with the semigroup algebra. Moreover, we define the cohomology of a twisted Rota-Baxter family operator. This cohomology can also be viewed as the cohomology of a certain Hom-$\\Omega$-associative algebra with coefficients in a suitable bimodule."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.20175","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/2410.20175/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"}