{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:27:59Z","timestamp":1760232479403,"version":"build-2065373602"},"reference-count":51,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2022,11,2]],"date-time":"2022-11-02T00:00:00Z","timestamp":1667347200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Department of Science and Technology","award":["00000"],"award-info":[{"award-number":["00000"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We characterize the dimension of Lie algebras of white noise operators containing the quantum white noise derivatives of the conservation operator. We establish isomorphisms to filiform Lie algebras, Engel-type algebras, and solvable Lie algebras with Heisenberg nilradical and Abelian nilradical. A new class of solvable Lie algebras is proposed, those having an Engel-type algebra as nilradical. This arises in white noise analysis as a 2n+3-dimensional Lie algebra containing the identity operator, annihilation operators, creation operators (Heisenberg algebra), number operator, and Gross Laplacian.<\/jats:p>","DOI":"10.3390\/sym14112301","type":"journal-article","created":{"date-parts":[[2022,11,3]],"date-time":"2022-11-03T04:11:31Z","timestamp":1667448691000},"page":"2301","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On Solvable Lie Algebras of White Noise Operators"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8400-0416","authenticated-orcid":false,"given":"Wolfgang","family":"Bock","sequence":"first","affiliation":[{"name":"Fachbereich Mathematik, Technische Universit\u00e4t Kaiserslautern, Gottlieb-Daimler-Strasse 48, 67663 Kaiserslautern, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Janeth","family":"Canama","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, College of Science and Mathematics, Mindanao State University-Iligan Institute of Technology, Andres Bonifacio Avenue, Iligan City 9200, Philippines"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gaudencio","family":"Petalcorin","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, College of Science and Mathematics, Mindanao State University-Iligan Institute of Technology, Andres Bonifacio Avenue, Iligan City 9200, Philippines"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Humphreys, J.E. 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