{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T15:55:09Z","timestamp":1774626909969,"version":"3.50.1"},"reference-count":5,"publisher":"World Scientific Pub Co Pte Lt","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[1999,10]]},"abstract":"<jats:p> We study the variety of Lie algebras defined by the identity [Formula: see text] over a field of characteristic zero. We prove that, as in the associative case, in the nth cocharacter \u03c7<jats:sub>n<\/jats:sub> of this variety, every irreducible S<jats:sub>n<\/jats:sub>-character appears with polynomially bounded multiplicity (not greater than n<jats:sup>2<\/jats:sup>). Anyway, surprisingly enough, we also show that the colength of this variety, i.e.\u00a0the total number of irreducibles appearing in \u03c7<jats:sub>n<\/jats:sub> is asymptotically equal to [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s0218196799000291","type":"journal-article","created":{"date-parts":[[2002,7,27]],"date-time":"2002-07-27T11:05:54Z","timestamp":1027767954000},"page":"483-491","source":"Crossref","is-referenced-by-count":6,"title":["ON THE COLENGTH OF A VARIETY OF LIE ALGEBRAS"],"prefix":"10.1142","volume":"09","author":[{"given":"A.","family":"GIAMBRUNO","sequence":"first","affiliation":[{"name":"Dipartimento di Matematica e Applicazioni, Universit\u00e0 di Palermo, 90123 Palermo, Italy"}]},{"given":"S.","family":"MISHCHENKO","sequence":"additional","affiliation":[{"name":"Department of Algebra and Geometric Computations, Faculty of Mathematics and Mechanics, Ulyanovsk State University, Ulyanovsk\u00a0432100, Russia"}]},{"given":"M.","family":"ZAICEV","sequence":"additional","affiliation":[{"name":"Department of Algebra, Faculty of Mathematics and Mechanics, Moscow State University,  Moscow, 119899, Russia"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"p_3","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(83)90167-9"},{"issue":"6","key":"p_5","first-page":"25","volume":"45","author":"Mishchenko S. P.","year":"1990","journal-title":"Uspekhi Mat. Nauk"},{"key":"p_6","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1971-12869-0"},{"issue":"12","key":"p_7","first-page":"1063","volume":"25","author":"Volichenko I. B.","year":"1981","journal-title":"Dokl. Akad. Nauk Belarusi"},{"issue":"3","key":"p_8","first-page":"40","volume":"25","author":"Volichenko I. B.","year":"1984","journal-title":"Sibirskii Mathematicheskii Zhurnal"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196799000291","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T21:55:50Z","timestamp":1565128550000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196799000291"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1999,10]]},"references-count":5,"journal-issue":{"issue":"05","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[1999,10]]}},"alternative-id":["10.1142\/S0218196799000291"],"URL":"https:\/\/doi.org\/10.1142\/s0218196799000291","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[1999,10]]}}}