关于自由李代数中乘积$[L_2，L_2，L_1]$的维数

IF 0.7 Q2 MATHEMATICS

International Journal of Group Theory Pub Date : 2017-06-09 DOI:10.22108/IJGT.2017.21481

Nil Mansuroğlu

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引用次数: 0

摘要

设$L$是域$F$上秩为$rgeq2$的自由李代数，设$L_n$表示$L的次$n$齐次分量$‎. ‎利用域$F上元李代数导出的自由中心第二理想的相应齐次和精细齐次分量的维数$‎, ‎我们确定$[L_2，L_2，L_1]的维数$‎. ‎此外‎, ‎通过这种方法‎, ‎我们证明了特征域$2$上的$[L_2，L_2，L_1]$的维数不同于特征域$2以外的域上的维数。

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On the dimension of the product $[L_2,L_2,L_1]$ in free Lie algebras

Let $L$ be a free Lie algebra of rank $rgeq2$ 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 $2$.

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来源期刊

International Journal of Group Theory MATHEMATICS-

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

30 weeks

期刊介绍： International Journal of Group Theory (IJGT) is an international mathematical journal founded in 2011. IJGT carries original research articles in the field of group theory, a branch of algebra. IJGT aims to reflect the latest developments in group theory and promote international academic exchanges.