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http://dx.doi.org/10.4134/BKMS.b160012

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)
Publication Information
Bulletin of the Korean Mathematical Society / v.54, no.2, 2017 , pp. 455-461 More about this Journal
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 $n{\geq}1$.
Keywords
factor Lie algebra; n-isoclinism; nilpotent Lie algebra;
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Times Cited By KSCI : 1  (Citation Analysis)
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