{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:08:47Z","timestamp":1760148527782,"version":"build-2065373602"},"reference-count":27,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2023,5,19]],"date-time":"2023-05-19T00:00:00Z","timestamp":1684454400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["11771135","21C0498","2019-TD-15"],"award-info":[{"award-number":["11771135","21C0498","2019-TD-15"]}]},{"name":"Hunan Provincial Department of Education","award":["11771135","21C0498","2019-TD-15"],"award-info":[{"award-number":["11771135","21C0498","2019-TD-15"]}]},{"name":"scientific research and innovation team of Hunnan Institute of Science and Technology","award":["11771135","21C0498","2019-TD-15"],"award-info":[{"award-number":["11771135","21C0498","2019-TD-15"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We define a four-dimensional Lie algebra g in this paper and then prove that this Lie algebra is solvable but not nilpotent. Due to the fact that g is a Lie algebra, \u2200x,y\u2208g,[x,y]=\u2212[y,x], that is, the operation [,] has anti symmetry. Symmetry is a very important law, and antisymmetry is also a very important law. We studied the structure of Poisson algebras on g using the matrix method. We studied the necessary and sufficient conditions for the automorphism of this class of Lie algebras, and give the decomposition of its automorphism group by Aut(g)=G3G1G2G3G4G7G8G5, or Aut(g)=G3G1G2G3G4G7G8G5G6, or Aut(g)=G3G1G2G3G4G7G8G5G3, where Gi is a commutative subgroup of Aut(g). We give some subgroups of g\u2019s automorphism group and systematically studied the properties of these subgroups.<\/jats:p>","DOI":"10.3390\/sym15051115","type":"journal-article","created":{"date-parts":[[2023,5,19]],"date-time":"2023-05-19T09:23:10Z","timestamp":1684488190000},"page":"1115","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Study on Poisson Algebra and Automorphism of a Special Class of Solvable Lie Algebras"],"prefix":"10.3390","volume":"15","author":[{"given":"Demin","family":"Yu","sequence":"first","affiliation":[{"name":"School of Mathematics, Hunan Institute of Science and Technology, Yueyang 414006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chan","family":"Jiang","sequence":"additional","affiliation":[{"name":"School of Mathematics, Hunan Institute of Science and Technology, Yueyang 414006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiejing","family":"Ma","sequence":"additional","affiliation":[{"name":"School of Mathematics, Hunan Institute of Science and Technology, Yueyang 414006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,5,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"849","DOI":"10.1007\/s11425-016-5127-4","article-title":"DG Poisson algebra and its universal enveloping algebra","volume":"59","author":"Wang","year":"2016","journal-title":"Sci. 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