On the Structure of Factor Lie Algebras

Abstract

Abstract. The Lie algebra analogue of Schur's result which is proved by Moneyhun in 1994, states that if L is a Lie algebra such that dimL/Z(L) = n, then dimL (2) = 1 2 n(n − 1) − s for some non-negative integer s. In the present paper, we determine the structure of central factor (for s = 0) and the factor Lie algebra L/Z 2 (L) (for all s ≥ 0) of a finite dimensional nilpotent Lie algebra L, with n-dimensional central factor. Furthermore, by using the concept of n-isoclinism, we discuss an upper bound for the dimension of L/Zn(L) in terms of dimL (n+1) , when the factor Lie algebra L/Zn(L) is finitely generated and n ≥ 1.