%0 Journal Article
%T On the dimension of the product $[L_2,L_2,L_1]$ in free Lie algebras
%J International Journal of Group Theory
%I University of Isfahan
%Z 2251-7650
%A Mansuroğlu, Nil
%D 2018
%\ 06/01/2018
%V 7
%N 2
%P 45-50
%! On the dimension of the product $[L_2,L_2,L_1]$ in free Lie algebras
%K Free Lie algebra
%K homogeneous and fine homogeneous components
%K free centre-by-metabelian Lie algebra
%K second derived ideal
%R 10.22108/ijgt.2017.21481
%X Let $L$ be a free Lie algebra of rank $r\geq2$ over a field $F$ and let $L_n$ denote the degree $n$ homogeneous component of $L$. By using the dimensions of the corresponding homogeneous and fine homogeneous components of the second derived ideal of free centre-by-metabelian Lie algebra over a field $F$, we determine the dimension of $[L_2,L_2,L_1]$. Moreover, by this method, we show that the dimension of $[L_2,L_2,L_1]$ over a field of characteristic $2$ is different from the dimension over a field of characteristic other than $2$.
%U https://ijgt.ui.ac.ir/article_21481_0b392ad1ffab7cd79272442ecc91712c.pdf