{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,6]],"date-time":"2025-05-06T04:00:49Z","timestamp":1746504049635,"version":"3.40.4"},"reference-count":16,"publisher":"World Scientific Pub Co Pte Ltd","issue":"03","funder":[{"name":"Young Scientists and Post-Doctoral Researchers - 2","award":["KP-06-N-32\/1"],"award-info":[{"award-number":["KP-06-N-32\/1"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2025,5]]},"abstract":"<jats:p> Let [Formula: see text] and [Formula: see text] be, respectively, the 2-generated free metabelian associative and Lie algebra over the field of complex numbers. In the associative case we find a finite set of generators of the algebra [Formula: see text] of the dihedral group of order [Formula: see text], [Formula: see text]. In the Lie case we find a minimal system of generators as a [Formula: see text]-module of the [Formula: see text]-invariants [Formula: see text] in the commutator ideal [Formula: see text] of [Formula: see text]. In both cases we compute the Hilbert (or Poincar\u00e9) series of the algebras [Formula: see text] and [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s0218196725500079","type":"journal-article","created":{"date-parts":[[2025,1,24]],"date-time":"2025-01-24T07:56:46Z","timestamp":1737705406000},"page":"343-355","source":"Crossref","is-referenced-by-count":0,"title":["Noncommutative invariants of dihedral groups"],"prefix":"10.1142","volume":"35","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6769-6757","authenticated-orcid":false,"given":"Vesselin","family":"Drensky","sequence":"first","affiliation":[{"name":"Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-9334-4367","authenticated-orcid":false,"given":"Boyan","family":"Kostadinov","sequence":"additional","affiliation":[{"name":"Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2025,3,10]]},"reference":[{"key":"S0218196725500079BIB002","doi-asserted-by":"publisher","DOI":"10.1515\/9783110566659"},{"key":"S0218196725500079BIB003","doi-asserted-by":"publisher","DOI":"10.1017\/S0017089500020024"},{"key":"S0218196725500079BIB004","doi-asserted-by":"publisher","DOI":"10.2307\/2372597"},{"key":"S0218196725500079BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2016.05.022"},{"key":"S0218196725500079BIB006","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1994-1181161-3"},{"first-page":"14","volume-title":"Math. and Education in Math., Proc. of the 24-th Spring Conf. of the Union of Bulgar. Mathematicians","author":"Drensky V.","key":"S0218196725500079BIB007"},{"key":"S0218196725500079BIB008","series-title":"Graduate Course in Algebra","volume-title":"Free Algebras and PI-algebras","author":"Drensky V.","year":"1999"},{"key":"S0218196725500079BIB009","doi-asserted-by":"publisher","DOI":"10.1007\/s00009-020-01582-8"},{"key":"S0218196725500079BIB010","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/043\/810646"},{"key":"S0218196725500079BIB011","series-title":"Cambridge Studies in Advanced Mathematics","volume-title":"Reflection Groups and Coxeter Groups","volume":"29","author":"Humphreys J. E.","year":"1992"},{"key":"S0218196725500079BIB013","doi-asserted-by":"publisher","DOI":"10.1016\/0022-4049(84)90079-3"},{"key":"S0218196725500079BIB014","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196795000227"},{"volume-title":"Vorlesungen \u00fcber das Ikosaeder und die Aufl\u00f6sung der Gleichungen vom f\u00fcnften Grade","year":"1884","author":"Klein F.","key":"S0218196725500079BIB015"},{"volume-title":"Lectures on the Icosahedron and the Solution of Equations of the Fifth Degree","year":"1956","author":"Klein F.","key":"S0218196725500079BIB016"},{"key":"S0218196725500079BIB020","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1954-028-3"},{"key":"S0218196725500079BIB021","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0095644"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196725500079","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,5]],"date-time":"2025-05-05T03:26:11Z","timestamp":1746415571000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0218196725500079"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,3,10]]},"references-count":16,"journal-issue":{"issue":"03","published-print":{"date-parts":[[2025,5]]}},"alternative-id":["10.1142\/S0218196725500079"],"URL":"https:\/\/doi.org\/10.1142\/s0218196725500079","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"type":"print","value":"0218-1967"},{"type":"electronic","value":"1793-6500"}],"subject":[],"published":{"date-parts":[[2025,3,10]]}}}