PRIMITIVE SETS OF FN / R LIE ALGEBRAS

Abstract: Let F_n be the free Lie algebra freely generated by a set {x_1,x_2,?,x_n } and let R be a verbal ideal of F_n. We prove that if W is a primitive subset of F_n/R which all of its elements do not involve x_n then W is primitive in F_(n-1)/R ^ , where R ^=RnF_(n-1).

Keywords: Free Lie algebras, solvable, nilpotent (super)algebras.