@article {
author = {Mansuroğlu, Nil},
title = {On the dimension of the product $[L_2,L_2,L_1]$ in free Lie algebras},
journal = {International Journal of Group Theory},
volume = {7},
number = {2},
pages = {45-50},
year = {2018},
publisher = {University of Isfahan},
issn = {2251-7650},
eissn = {2251-7669},
doi = {10.22108/ijgt.2017.21481},
abstract = {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 $2$.},
keywords = {Free Lie algebra,homogeneous and fine homogeneous components,free centre-by-metabelian Lie algebra,second derived ideal},
url = {https://ijgt.ui.ac.ir/article_21481.html},
eprint = {https://ijgt.ui.ac.ir/article_21481_0b392ad1ffab7cd79272442ecc91712c.pdf}
}