{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:33:10Z","timestamp":1760149990755,"version":"build-2065373602"},"reference-count":24,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2023,9,29]],"date-time":"2023-09-29T00:00:00Z","timestamp":1695945600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Universities Key Laboratory of System Modeling and Data Mining in Guizhou Province","award":["2023013","[2018]1020","QJJ[2023]063","GYU-KY-2023"],"award-info":[{"award-number":["2023013","[2018]1020","QJJ[2023]063","GYU-KY-2023"]}]},{"name":"Foundation of Science and Technology of Guizhou Province","award":["2023013","[2018]1020","QJJ[2023]063","GYU-KY-2023"],"award-info":[{"award-number":["2023013","[2018]1020","QJJ[2023]063","GYU-KY-2023"]}]},{"name":"Guizhou University of Finance and Economics introduced talent research projects","award":["2023013","[2018]1020","QJJ[2023]063","GYU-KY-2023"],"award-info":[{"award-number":["2023013","[2018]1020","QJJ[2023]063","GYU-KY-2023"]}]},{"name":"Scientific Research Foundation for Science &amp; Technology Innovation Talent Team of the Intelligent Computing and Monitoring of Guizhou Province","award":["2023013","[2018]1020","QJJ[2023]063","GYU-KY-2023"],"award-info":[{"award-number":["2023013","[2018]1020","QJJ[2023]063","GYU-KY-2023"]}]},{"name":"Doctoral Research Start-up Fund of Guiyang University","award":["2023013","[2018]1020","QJJ[2023]063","GYU-KY-2023"],"award-info":[{"award-number":["2023013","[2018]1020","QJJ[2023]063","GYU-KY-2023"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, the notion of generalized Reynolds operators on Lie-Yamaguti algebras is introduced, and the cohomology of a generalized Reynolds operator is established. The formal deformations of a generalized Reynolds operator are studied using the first cohomology group. Then, we show that a Nijenhuis operator on a Lie-Yamaguti algebra gives rise to a representation of the deformed Lie-Yamaguti algebra and a 2-cocycle. Consequently, the identity map will be a generalized Reynolds operator on the deformed Lie-Yamaguti algebra. We also introduce the notion of a Reynolds operator on a Lie-Yamaguti algebra, which can serve as a special case of generalized Reynolds operators on Lie-Yamaguti algebras.<\/jats:p>","DOI":"10.3390\/axioms12100934","type":"journal-article","created":{"date-parts":[[2023,9,29]],"date-time":"2023-09-29T07:42:08Z","timestamp":1695973328000},"page":"934","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Generalized Reynolds Operators on Lie-Yamaguti Algebras"],"prefix":"10.3390","volume":"12","author":[{"given":"Wen","family":"Teng","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiulin","family":"Jin","sequence":"additional","affiliation":[{"name":"School of Science, Guiyang University, Guiyang 550005, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fengshan","family":"Long","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,9,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"731","DOI":"10.2140\/pjm.1960.10.731","article-title":"An analytic problem whose solution follows from a simple algebraic identity","volume":"10","author":"Baxter","year":"1960","journal-title":"Pac. 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