Findik, SehmusKelekci, Osman2024-11-072024-11-0720210218-19671793-6500https://doi.org/10.1142/S0218196721500521https://hdl.handle.net/11480/15497Let X and Y be two generic traceless matrices of size 2 x 2 with entries from a commutative associative polynomial algebra over a field K of characteristic zero. Consider the associative unitary algebra W, and its Lie subalgebra L generated by X and Y over the field K. It is well known that the center C(W) = K[t,u,v] of W is the polynomial algebra generated by the algebraically independent commuting elements t = tr(X-2)I-2, u = tr(Y-2)I-2, v = tr(XY)I-2. We call a polynomial p is an element of W symmetric, if p(X,Y ) = p(Y,X). The set of symmetric polynomials is equal to the algebra W-S2 of invariants of symmetric group S-2. Similarly, we define the Lie algebra L-S2 of symmetric polynomials in the Lie algebra L. We give the description of the algebras W-S2 and L-S2, and we provide finite sets of free generators for W-S2, and [L,L](S2) as K[t + u,tu,v]-modules.eninfo:eu-repo/semantics/closedAccessLie algebrassymmetric polynomialsgeneric matricesArticle3171433144210.1142/S02181967215005212-s2.0-85108980345Q2WOS:000717064200007Q3