On the dimension of the product $[L_2,L_2,L_1]$ in free Lie algebras
نویسندگان
1 National University of Ireland Galway
doi
10.22108/ijgt.2017.21481چکیده
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 $2$.
