{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:41:15Z","timestamp":1760143275521,"version":"build-2065373602"},"reference-count":243,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2024,1,27]],"date-time":"2024-01-27T00:00:00Z","timestamp":1706313600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In the present paper, we review the progress of the project of the classification and construction of invariant differential operators for non-compact, semisimple Lie groups. Our starting point is the class of algebras which we called earlier \u2018conformal Lie algebras\u2019 (CLA), which have very similar properties to the conformal algebras of Minkowski space-time, though our aim is to go beyond this class in a natural way. For this purpose, we introduced recently the new notion of a parabolic relation between two non-compact, semi-simple Lie algebras G and G\u2032 that have the same complexification and possess maximal parabolic subalgebras with the same complexification.<\/jats:p>","DOI":"10.3390\/sym16020151","type":"journal-article","created":{"date-parts":[[2024,1,29]],"date-time":"2024-01-29T04:57:07Z","timestamp":1706504227000},"page":"151","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Canonical Construction of Invariant Differential Operators: A Review"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1456-5753","authenticated-orcid":false,"given":"Vladimir K.","family":"Dobrev","sequence":"first","affiliation":[{"name":"Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, 72 Tsarigradsko Chaussee, 1784 Sofia, Bulgaria"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,1,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Gomberoff, A., and Marolf, D. 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