{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T08:50:15Z","timestamp":1775465415692,"version":"3.50.1"},"reference-count":25,"publisher":"World Scientific Pub Co Pte Ltd","issue":"08","funder":[{"name":"the Russian Science Foundation","award":["RSF 24-21-00102"],"award-info":[{"award-number":["RSF 24-21-00102"]}]},{"name":"the Program of Fundamental Research RAS","award":["FWNF-2022-0002"],"award-info":[{"award-number":["FWNF-2022-0002"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2024,12]]},"abstract":"<jats:p> If A is an associative algebra, then we can define the adjoint Lie algebra [Formula: see text] and Jordan algebra [Formula: see text]. It is easy to see that any associative Rota\u2013Baxter (RB) operator on A induces a Lie and Jordan RB operator on [Formula: see text] and [Formula: see text], respectively. Are there Lie (Jordan) RB operators, which are not associative RB operators? In this paper, we explore these questions for the Sweedler algebra [Formula: see text], which is a 4-dimensional non-commutative Hopf algebra. More precisely, we describe the RB operators on the adjoint Lie algebra [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s0218196724500462","type":"journal-article","created":{"date-parts":[[2024,9,13]],"date-time":"2024-09-13T06:59:36Z","timestamp":1726210776000},"page":"1159-1189","source":"Crossref","is-referenced-by-count":1,"title":["Lie Rota\u2013Baxter operators on the Sweedler algebra\u00a0H4"],"prefix":"10.1142","volume":"34","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-4531-6715","authenticated-orcid":false,"given":"Valeriy G.","family":"Bardakov","sequence":"first","affiliation":[{"name":"Sobolev Institute of Mathematics, Acad. 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