# ON THE STRUCTURE OF FACTOR LIE ALGEBRAS

• Arabyani, Homayoon (Department of Mathematics Neyshabur Branch Islamic Azad University) ;
• Panbehkar, Farhad (Department of Mathematics Neyshabur Branch Islamic Azad University) ;
• Safa, Hesam (Department of Mathematics Faculty of Basic Sciences University of Bojnord)
• Published : 2017.03.31
• 142 28

#### 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 $dimL_{(2)}={\frac{1}{2}}n(n-1)-s$ 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 $s{\geq}0$) 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 $L/Z_n(L)$ in terms of $dimL_{(n+1)}$, when the factor Lie algebra $L/Z_n(L)$ is finitely generated and $n{\geq}1$.

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