{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,4]],"date-time":"2026-03-04T05:24:34Z","timestamp":1772601874827,"version":"3.50.1"},"reference-count":10,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2021,3]]},"abstract":"<jats:p> We study the representation theory of finite-dimensional [Formula: see text]-Lie algebras over the complex field. We derive an [Formula: see text]-Lie version of the classical Lie\u2019s theorem, i.e., any finite-dimensional irreducible module of a soluble [Formula: see text]-Lie algebra is 1-dimensional (1D). We also prove that indecomposable modules of some 3D [Formula: see text]-Lie algebras could be parametrized by the complex field and nilpotent matrices. We introduce the notion of a tailed derivation of a nonassociative algebra [Formula: see text] and prove that if [Formula: see text] is a Lie algebra, then there exists a one-to-one correspondence between tailed derivations of [Formula: see text] and 1D [Formula: see text]-extensions of [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s021819672150017x","type":"journal-article","created":{"date-parts":[[2020,11,24]],"date-time":"2020-11-24T10:07:16Z","timestamp":1606212436000},"page":"325-339","source":"Crossref","is-referenced-by-count":8,"title":["Representations of \u03c9-Lie algebras and tailed derivations of Lie algebras"],"prefix":"10.1142","volume":"31","author":[{"given":"Runxuan","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2020,12,17]]},"reference":[{"key":"S021819672150017XBIB001","doi-asserted-by":"publisher","DOI":"10.1007\/s00605-013-0537-7"},{"key":"S021819672150017XBIB002","first-page":"51","volume":"605","author":"Bobie\u0144ski M.","year":"2007","journal-title":"J. Reine Angew. Math."},{"key":"S021819672150017XBIB003","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511614910"},{"key":"S021819672150017XBIB004","doi-asserted-by":"publisher","DOI":"10.4171\/PM\/1943"},{"key":"S021819672150017XBIB005","doi-asserted-by":"publisher","DOI":"10.1007\/s40840-015-0120-6"},{"key":"S021819672150017XBIB006","doi-asserted-by":"publisher","DOI":"10.1080\/00927872.2017.1327062"},{"key":"S021819672150017XBIB007","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1948-0024908-8"},{"key":"S021819672150017XBIB008","doi-asserted-by":"publisher","DOI":"10.1016\/j.geomphys.2006.10.008"},{"key":"S021819672150017XBIB009","doi-asserted-by":"publisher","DOI":"10.1016\/j.geomphys.2008.03.012"},{"key":"S021819672150017XBIB010","doi-asserted-by":"publisher","DOI":"10.1016\/j.geomphys.2010.03.005"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S021819672150017X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,12]],"date-time":"2021-04-12T09:23:11Z","timestamp":1618219391000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S021819672150017X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,12,17]]},"references-count":10,"journal-issue":{"issue":"02","published-print":{"date-parts":[[2021,3]]}},"alternative-id":["10.1142\/S021819672150017X"],"URL":"https:\/\/doi.org\/10.1142\/s021819672150017x","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,12,17]]}}}