Symmetric polynomials in free center-by-metabelian Lie algebras of rank 2

Abstract

Let [Formula: see text] be the free center-by-metabelian Lie algebra of rank 2 freely generated by the set [Formula: see text]. Let [Formula: see text] be the Lie subalgebra of symmetric polynomials in [Formula: see text], that is, [Formula: see text] consists of all the elements [Formula: see text] in [Formula: see text] such that [Formula: see text]. We give a linear basis and a minimal infinite generating set for [Formula: see text], thus extending results of Ş. Findik and N. Ögüşlü [Palindromes in the free metabelian Lie algebras, Internat. J. Algebra Comput. 29(5) (2019) 885–891].