{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T08:11:03Z","timestamp":1773389463073,"version":"3.50.1"},"reference-count":28,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2024,11,27]],"date-time":"2024-11-27T00:00:00Z","timestamp":1732665600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["12371256"],"award-info":[{"award-number":["12371256"]}]},{"name":"National Natural Science Foundation of China","award":["11971475"],"award-info":[{"award-number":["11971475"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, we search for some approaches for generating (1+1)-dimensional, (2+1)-dimensional and (3+1)-dimensional integrable equations by making use of various Lie algebras and the corresponding loop algebras under the frame of the Tu scheme. The well-known modified KdV equation, the heat conduction equation, the nonlinear Schr\u00f6dinger equation, the (2+1)-dimensional cylindrical dissipative Zaboloskaya\u2013Khokhlov equation and the (3+1)-dimensional heavenly equation are obtained, respectively. In addition, some new isospectral integrable hierarchies and their nonisospectral integrable hierarchies are singled out. All the Lie algebras and their loop algebras presented in the paper can be extensively applied to investigate other integrable hierarchies of evolution equations.<\/jats:p>","DOI":"10.3390\/axioms13120830","type":"journal-article","created":{"date-parts":[[2024,11,27]],"date-time":"2024-11-27T10:05:56Z","timestamp":1732701956000},"page":"830","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Few Kinds of Loop Algebras and Some Applications"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1339-4999","authenticated-orcid":false,"given":"Yanmei","family":"Sun","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Weifang University, Weifang 261061, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Weiwei","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Weifang University, Weifang 261061, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9316-030X","authenticated-orcid":false,"given":"Nina","family":"Xue","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Weifang University, Weifang 261061, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yufeng","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mathematics, China University of Mining and Technology, Xuzhou 221116, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,11,27]]},"reference":[{"key":"ref_1","unstructured":"Magri, F. 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