Palindromes in the free metabelian Lie algebras
Şehmus Fındık, Nazar Şahi̇n Öğüşlü · International Journal of Algebra and Computation · 2019
A palindrome, in general, is a word in a fixed alphabet which is preserved when taken in reverse order. Let [Formula: see text] be the free metabelian Lie algebra over a field of characteristic zero generated by [Formula: see text]. We propose the following definition of palindromes in the setting of Lie algebras: An element [Formula: see text] is called a palindrome if it is preserved under the change of generators; i.e. [Formula: see text]. We give a linear basis and an explicit infinite generating set for the Lie subalgebra of palindromes.