{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,1,18]],"date-time":"2024-01-18T13:49:30Z","timestamp":1705585770700},"reference-count":25,"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":[[2015,9]]},"abstract":"<jats:p> For any Lie algebra L over a field, its universal enveloping algebra U(L) can be embedded in a division ring \ud835\udd07(L) constructed by Lichtman. If U(L) is an Ore domain, \ud835\udd07(L) coincides with its ring of fractions. It is well known that the principal involution of L, x \u21a6 -x, can be extended to an involution of U(L), and Cimpric proved that this involution can be extended to one on \ud835\udd07(L). For a large class of noncommutative Lie algebras L over a field of characteristic zero, we show that \ud835\udd07(L) contains noncommutative free algebras generated by symmetric elements with respect to (the extension of) the principal involution. This class contains all noncommutative Lie algebras such that U(L) is an Ore domain. <\/jats:p>","DOI":"10.1142\/s0218196715500319","type":"journal-article","created":{"date-parts":[[2015,8,27]],"date-time":"2015-08-27T21:39:08Z","timestamp":1440711548000},"page":"1075-1106","source":"Crossref","is-referenced-by-count":2,"title":["Free symmetric algebras in division rings generated by enveloping algebras of Lie algebras"],"prefix":"10.1142","volume":"25","author":[{"given":"Vitor O.","family":"Ferreira","sequence":"first","affiliation":[{"name":"Department of Mathematics \u2014 IME, University of S\u00e3o Paulo, Caixa Postal 66281, S\u00e3o Paulo, SP, 05314-970, Brazil"}]},{"given":"Jairo Z.","family":"Gon\u00e7alves","sequence":"additional","affiliation":[{"name":"Department of Mathematics \u2014 IME, University of S\u00e3o Paulo, Caixa Postal 66281, S\u00e3o Paulo, SP, 05314-970, Brazil"}]},{"given":"Javier","family":"S\u00e1nchez","sequence":"additional","affiliation":[{"name":"Department of Mathematics \u2014 IME, University of S\u00e3o Paulo, Caixa Postal 66281, S\u00e3o Paulo, SP, 05314-970, Brazil"}]}],"member":"219","published-online":{"date-parts":[[2015,9,29]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-8693(03)00402-2"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1080\/00927879508825230"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2004.01.033"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/s3-11.1.511"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139087193"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1090\/gsm\/011"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2013.06.016"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1080\/00927872.2011.554934"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-96-03032-8"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1007\/s00029-014-0168-4"},{"key":"rf11","volume-title":"Lie Algebras","author":"Jacobson N.","year":"1979"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1007\/BF02218611"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0525-8"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4419-8616-0"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.1995.1332"},{"key":"rf16","first-page":"145","volume":"6","author":"Lichtman A. 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