论文标题
分级的谎言代数的成分最大级别和链链长度的代数
Constituents of graded Lie algebras of maximal class and chain lengths of thin Lie algebras
论文作者
论文摘要
薄的lie代数是无限维级的lie代数$ l = \ bigoplus_ {i = 1}^{\ infty} $，带有$ \ dim（l_1）= 2 $且满足封面属性：对于每个$ i $ $ $ $，每个nonnonnonnon nonnozero $ z \ in l_i $ $ $ $ $ $ $ $} $ [zl_1]因此，每个均质组件$ l_i $都是一维或二维的，在后一种情况下，称为钻石。因此，$ l_1 $是钻石，如果没有其他钻石，那么$ l $是最大级别的分级谎言代数。 我们提供了一些基于统一方法的最大级别级别的分级代数的基本事实的简单证明，重点是多项式解释。除此之外，我们确定了此代数的最基本参数的可能值，这是其最大的Metabelian商的维度。
Thin Lie algebras are infinite-dimensional graded Lie algebras $L=\bigoplus_{i=1}^{\infty}$, with $\dim(L_1)=2$ and satisfying a covering property: for each $i$, each nonzero $z\in L_i$ satisfies $[zL_1]=L_{i+1}$. It follows that each homogeneous components $L_i$ is either one- or two-dimensional, and in the latter case is called a diamond. Hence $L_1$ is a diamond, and if there are no other diamonds then $L$ is a graded Lie algebra of maximal class. We present simpler proofs of some fundamental facts on graded Lie algebras of maximal class, and on thin Lie algebras, based on a uniform method, with emphasis on a polynomial interpretation. Among else, we determine the possible values for the most fundamental parameter of such algebras, which is the dimension of their largest metabelian quotient.
