{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T21:13:48Z","timestamp":1775164428516,"version":"3.50.1"},"reference-count":18,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2025,4,14]],"date-time":"2025-04-14T00:00:00Z","timestamp":1744588800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"King Khalid University","award":["RGP2\/339\/45"],"award-info":[{"award-number":["RGP2\/339\/45"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper extends the notions of n-derivations and n-automorphisms from Lie algebras to nest algebras via exponential mappings. We establish necessary and sufficient conditions for triangularity, and examine the preservation of the radical, center, and ideals under these higher-order algebraic transformations. The induced group structures of n-automorphisms are explicitly characterized, including inner and non-abelian components. Several concrete examples demonstrate the applicability and depth of the theoretical findings.<\/jats:p>","DOI":"10.3390\/sym17040596","type":"journal-article","created":{"date-parts":[[2025,4,15]],"date-time":"2025-04-15T08:11:39Z","timestamp":1744704699000},"page":"596","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Advanced Structural Analysis of n-Derivations and n-Automorphisms in Nest Algebras via Exponential Mappings"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4167-3119","authenticated-orcid":false,"given":"Ali","family":"Al Khabyah","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9169-8488","authenticated-orcid":false,"family":"Nazim","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India"}]},{"given":"Shaheen","family":"Khan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India"}]}],"member":"1968","published-online":{"date-parts":[[2025,4,14]]},"reference":[{"key":"ref_1","unstructured":"Ringrose, J.R. 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Nachrichten"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1016\/j.laa.2005.02.004","article-title":"Lie triple derivations of TUHF algebras","volume":"403","author":"Ji","year":"2005","journal-title":"Linear Algebra Appl."},{"key":"ref_16","first-page":"425","article-title":"2-Local Lie isomorphisms of nest algebras","volume":"10","author":"Li","year":"2016","journal-title":"Oper. Matrices"},{"key":"ref_17","unstructured":"Power, S.C. (1992). Limit Algebras: An Introduction to Subalgebras of C*-Algebras, Longman Scientific & Technical."},{"key":"ref_18","first-page":"187","article-title":"On Commuting Automorphisms of Nest Algebras","volume":"4","year":"1980","journal-title":"J. Oper. 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