{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,26]],"date-time":"2025-03-26T04:01:37Z","timestamp":1742961697688,"version":"3.40.3"},"reference-count":22,"publisher":"World Scientific Pub Co Pte Ltd","issue":"02","funder":[{"DOI":"10.13039\/501100003593","name":"CNPq","doi-asserted-by":"crossref","award":["307184\/2023-4"],"award-info":[{"award-number":["307184\/2023-4"]}],"id":[{"id":"10.13039\/501100003593","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001807","name":"FAPESP","doi-asserted-by":"crossref","award":["2018\/23690-6"],"award-info":[{"award-number":["2018\/23690-6"]}],"id":[{"id":"10.13039\/501100001807","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2025,3]]},"abstract":"<jats:p> Let K be a field of characteristic zero and let [Formula: see text] be the 3-dimensional simple Lie algebra over K. In this paper, we describe a finite basis for the [Formula: see text]-graded identities of the adjoint representation of [Formula: see text], or equivalently, the [Formula: see text]-graded identities for the pair [Formula: see text]. We work with the canonical grading on [Formula: see text] and the only nontrivial [Formula: see text]-grading of the associative algebra [Formula: see text] induced by that on [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s0218196725500055","type":"journal-article","created":{"date-parts":[[2025,1,3]],"date-time":"2025-01-03T09:08:11Z","timestamp":1735895291000},"page":"289-309","source":"Crossref","is-referenced-by-count":0,"title":["Graded identities of the adjoint representation of \ud835\udd30\ud835\udd292(K)"],"prefix":"10.1142","volume":"35","author":[{"ORCID":"https:\/\/orcid.org\/0009-0007-1666-7124","authenticated-orcid":false,"given":"C\u00e1ssia","family":"Sampaio","sequence":"first","affiliation":[{"name":"Department of Mathematics, State University of Campinas, 651 S\u00e9rgio Buarque de Holanda, 13083-859 Campinas, SP, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1819-0100","authenticated-orcid":false,"given":"Plamen","family":"Koshlukov","sequence":"additional","affiliation":[{"name":"Department of Mathematics, State University of Campinas, 651 S\u00e9rgio Buarque de Holanda, 13083-859 Campinas, SP, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2025,2,18]]},"reference":[{"key":"S0218196725500055BIB001","doi-asserted-by":"publisher","DOI":"10.1080\/03081087.2016.1202185"},{"key":"S0218196725500055BIB002","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2024.06.008"},{"key":"S0218196725500055BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/B978-0-12-428780-8.50016-7"},{"key":"S0218196725500055BIB004","doi-asserted-by":"publisher","DOI":"10.1007\/BF02808074"},{"key":"S0218196725500055BIB005","doi-asserted-by":"publisher","DOI":"10.1007\/BF01669018"},{"key":"S0218196725500055BIB006","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(84)90121-2"},{"key":"S0218196725500055BIB007","doi-asserted-by":"publisher","DOI":"10.1007\/BF01669108"},{"key":"S0218196725500055BIB008","first-page":"313","volume":"8","author":"Genov G. K.","year":"1982","journal-title":"Serdica"},{"key":"S0218196725500055BIB009","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2013.05.009"},{"key":"S0218196725500055BIB010","doi-asserted-by":"publisher","DOI":"10.1007\/BF01978692"},{"key":"S0218196725500055BIB011","doi-asserted-by":"publisher","DOI":"10.1090\/mmono\/087"},{"key":"S0218196725500055BIB012","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.1996.6850"},{"key":"S0218196725500055BIB013","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.2000.8738"},{"key":"S0218196725500055BIB014","doi-asserted-by":"publisher","DOI":"10.1142\/S021819670800469X"},{"key":"S0218196725500055BIB015","doi-asserted-by":"publisher","DOI":"10.1007\/BF02785422"},{"issue":"1","key":"S0218196725500055BIB016","first-page":"497","volume":"38","author":"Koshlukov P.","year":"2012","journal-title":"Serdica Math. J."},{"key":"S0218196725500055BIB017","doi-asserted-by":"publisher","DOI":"10.1007\/BF02218641"},{"key":"S0218196725500055BIB018","doi-asserted-by":"publisher","DOI":"10.1090\/mmono\/138"},{"issue":"2","key":"S0218196725500055BIB019","first-page":"5","volume":"2004","author":"Repin D. V.","year":"2004","journal-title":"Vestn. Samar. Gos. Univ., Estestvennonauchn. Ser."},{"key":"S0218196725500055BIB020","doi-asserted-by":"publisher","DOI":"10.1007\/BF01978983"},{"key":"S0218196725500055BIB021","doi-asserted-by":"publisher","DOI":"10.1007\/BF01979196"},{"key":"S0218196725500055BIB022","doi-asserted-by":"publisher","DOI":"10.1093\/qmath\/21.3.297"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196725500055","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,25]],"date-time":"2025-03-25T03:27:55Z","timestamp":1742873275000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0218196725500055"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,2,18]]},"references-count":22,"journal-issue":{"issue":"02","published-print":{"date-parts":[[2025,3]]}},"alternative-id":["10.1142\/S0218196725500055"],"URL":"https:\/\/doi.org\/10.1142\/s0218196725500055","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"type":"print","value":"0218-1967"},{"type":"electronic","value":"1793-6500"}],"subject":[],"published":{"date-parts":[[2025,2,18]]}}}