{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,3]],"date-time":"2022-04-03T00:29:53Z","timestamp":1648945793424},"reference-count":15,"publisher":"World Scientific Pub Co Pte Lt","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2018,9]]},"abstract":"<jats:p> Let [Formula: see text] be a relatively free Lie algebra of finite rank [Formula: see text], with [Formula: see text], [Formula: see text] be the completion of [Formula: see text] with respect to the topology defined by the lower central series [Formula: see text] of [Formula: see text] and [Formula: see text], with [Formula: see text]. We prove that, with respect to the formal power series topology, the automorphism group [Formula: see text] of [Formula: see text] is dense in the automorphism group [Formula: see text] of [Formula: see text] if and only if [Formula: see text] is nilpotent. Furthermore, we show that there exists a dense subgroup of [Formula: see text] generated by [Formula: see text] and a finite set of IA-automorphisms if and only if [Formula: see text] is generated by [Formula: see text] and a finite set of IA-automorphisms independent upon [Formula: see text] for all [Formula: see text]. We apply our study to several varieties of Lie algebras. <\/jats:p>","DOI":"10.1142\/s0218196718500479","type":"journal-article","created":{"date-parts":[[2018,6,25]],"date-time":"2018-06-25T03:32:35Z","timestamp":1529897555000},"page":"1091-1100","source":"Crossref","is-referenced-by-count":0,"title":["Automorphisms of the completion of relatively free Lie algebras"],"prefix":"10.1142","volume":"28","author":[{"given":"C. E.","family":"Kofinas","sequence":"first","affiliation":[{"name":"Faculty of Sciences, Department of Mathematics, Aristotle University of Thessaloniki, GR 541 24, Thessaloniki, Greece"}]}],"member":"219","published-online":{"date-parts":[[2018,9,17]]},"reference":[{"key":"S0218196718500479BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(83)90160-6"},{"key":"S0218196718500479BIB003","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1993-063-5"},{"key":"S0218196718500479BIB004","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1990-015-1"},{"key":"S0218196718500479BIB005","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0092296"},{"key":"S0218196718500479BIB006","doi-asserted-by":"publisher","DOI":"10.1080\/00927871003601667"},{"key":"S0218196718500479BIB007","doi-asserted-by":"publisher","DOI":"10.1080\/00927870903004360"},{"key":"S0218196718500479BIB008","doi-asserted-by":"publisher","DOI":"10.1093\/qmath\/hav008"},{"key":"S0218196718500479BIB009","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196716500326"},{"key":"S0218196718500479BIB010","doi-asserted-by":"publisher","DOI":"10.1142\/S0219498818500779"},{"key":"S0218196718500479BIB011","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/52.1.157"},{"issue":"3","key":"S0218196718500479BIB012","first-page":"193","volume":"3","author":"Papistas A. I.","year":"1996","journal-title":"Algebra Colloq."},{"key":"S0218196718500479BIB013","doi-asserted-by":"publisher","DOI":"10.1017\/S0024610701002058"},{"key":"S0218196718500479BIB014","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196704001761"},{"key":"S0218196718500479BIB015","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196708004408"},{"key":"S0218196718500479BIB016","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511565953"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196718500479","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T19:38:01Z","timestamp":1565120281000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196718500479"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,9]]},"references-count":15,"journal-issue":{"issue":"06","published-online":{"date-parts":[[2018,9,17]]},"published-print":{"date-parts":[[2018,9]]}},"alternative-id":["10.1142\/S0218196718500479"],"URL":"https:\/\/doi.org\/10.1142\/s0218196718500479","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,9]]}}}