{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,1]],"date-time":"2025-06-01T19:41:33Z","timestamp":1748806893244},"reference-count":15,"publisher":"World Scientific Pub Co Pte Ltd","issue":"07","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2021,11]]},"abstract":"<jats:p> Let [Formula: see text] and [Formula: see text] be two generic traceless matrices of size [Formula: see text] with entries from a commutative associative polynomial algebra over a field [Formula: see text] of characteristic zero. Consider the associative unitary algebra [Formula: see text], and its Lie subalgebra [Formula: see text] generated by [Formula: see text] and [Formula: see text] over the field [Formula: see text]. It is well known that the center [Formula: see text] of [Formula: see text] is the polynomial algebra generated by the algebraically independent commuting elements [Formula: see text], [Formula: see text], [Formula: see text]. We call a polynomial [Formula: see text] symmetric, if [Formula: see text]. The set of symmetric polynomials is equal to the algebra [Formula: see text] of invariants of symmetric group [Formula: see text]. Similarly, we define the Lie algebra [Formula: see text] of symmetric polynomials in the Lie algebra [Formula: see text]. We give the description of the algebras [Formula: see text] and [Formula: see text], and we provide finite sets of free generators for [Formula: see text], and [Formula: see text] as [Formula: see text]-modules. <\/jats:p>","DOI":"10.1142\/s0218196721500521","type":"journal-article","created":{"date-parts":[[2021,6,29]],"date-time":"2021-06-29T01:52:45Z","timestamp":1624931565000},"page":"1433-1442","source":"Crossref","is-referenced-by-count":2,"title":["Symmetric polynomials of algebras related with 2 \u00d7 2 generic traceless matrices"],"prefix":"10.1142","volume":"31","author":[{"given":"\u015eehmus","family":"F\u0131nd\u0131k","sequence":"first","affiliation":[{"name":"Department of Mathematics, \u00c7ukurova University, 01330 Balcal\u0131, Adana, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Osman","family":"Kelekci\u0307","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Ni\u011fde \u00d6mer Halisdemir University, 51240 Ni\u011fde, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2021,6,28]]},"reference":[{"key":"S0218196721500521BIB002","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-2008-013-4"},{"key":"S0218196721500521BIB003","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/s2-43.2.215"},{"key":"S0218196721500521BIB004","doi-asserted-by":"publisher","DOI":"10.1080\/03081088208817467"},{"key":"S0218196721500521BIB005","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1994-1181161-3"},{"key":"S0218196721500521BIB006","first-page":"49","volume":"14","author":"Drensky V.","year":"2012","journal-title":"Alg. 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