On the dimension of the product $[L_۲,L_۲,L_۱]$ in free Lie algebras
عنوان مقاله: On the dimension of the product $[L_۲,L_۲,L_۱]$ in free Lie algebras
شناسه ملی مقاله: JR_THEGR-7-2_007
منتشر شده در در سال 1397
شناسه ملی مقاله: JR_THEGR-7-2_007
منتشر شده در در سال 1397
مشخصات نویسندگان مقاله:
Nil Mansuroğlu - Ahi Evran University
خلاصه مقاله:
Nil Mansuroğlu - Ahi Evran University
Let $L$ be a free Lie algebra of rank $r\geq۲$ 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 $[L_۲,L_۲,L_۱]$. Moreover, by this method, we show that the dimension of $[L_۲,L_۲,L_۱]$ over a field of characteristic $۲$ is different from the dimension over a field of characteristic other than $۲$.
کلمات کلیدی: Free Lie algebra, homogeneous and fine homogeneous components, free centre-by-metabelian Lie algebra, second derived ideal
صفحه اختصاصی مقاله و دریافت فایل کامل: https://civilica.com/doc/1194978/