{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,11]],"date-time":"2026-02-11T13:38:54Z","timestamp":1770817134109,"version":"3.50.1"},"reference-count":16,"publisher":"World Scientific Pub Co Pte Ltd","issue":"08","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2024,12]]},"abstract":"<jats:p> Rota\u2013Baxter operators on groups have been recently defined in [L.\u00a0Guo, H.\u00a0Lang and Y.\u00a0 Sheng, Integration and geometrization of Rota\u2013Baxter Lie algebras, Adv. Math.\u00a0387 (2021) 107834], and they share a close connection with skew braces, as demonstrated in [V.\u00a0Bardakov and V.\u00a0Gubarev, Rota\u2013Baxter groups, skew left braces, and the Yang\u2013Baxter equation, J. Algebra\u00a0587 (2022) 328\u2013351]. In this paper, we classify all Rota\u2013Baxter operators of weight 1 on the Heisenberg Lie algebra of dimension 3 up to the Jordan canonical form of a [Formula: see text] matrix block by automorphisms of the Heisenberg Lie algebra. Using the fact that the exponential map from the Heisenberg Lie algebra to the Heisenberg group is bijective, we induce these operators on the Heisenberg group. Finally, we enumerate all skew left brace structures on the Heisenberg group induced by these Rota\u2013Baxter operators. <\/jats:p>","DOI":"10.1142\/s0218196724500474","type":"journal-article","created":{"date-parts":[[2024,9,13]],"date-time":"2024-09-13T06:59:36Z","timestamp":1726210776000},"page":"1191-1207","source":"Crossref","is-referenced-by-count":3,"title":["Rota\u2013Baxter operators and skew left brace structures over Heisenberg group"],"prefix":"10.1142","volume":"34","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8199-9335","authenticated-orcid":false,"given":"Nishant","family":"Rathee","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, Indian Institute of Science Education and Research, Mohali, Sector 81, SAS Nagar, P. O. 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