论文标题
小核心中心的衍生物代数为nilpotent
Nilpotent Lie algebras of derivations with the center of small corank
论文作者
论文摘要
令$ \ mathbb k $为特征零的字段，$ a $ a $ a $ a $ \ mathbb k $与分数$ r = \ text {frac}（a），$ \ text {der text {der} _ {\ mathbb {K} 令$ w（a）：= r \ text {der} _ {\ mathbb {k}} a $和$ l $ a nilpotent sublgebra等级$ n $上的$ r $ a $ r $ y elgebra $ w（a）。对于$ r中的$ l $，$，那么lie代数$ fl $包含在本地的nilpotent subemalgebra中，$ w（a）$等级$ n $ a $ n $ a $ a $ a $ a $ a $ a $ a $ a $ r $ a field $R。$也可以证明，也可以证明，lie代数$ fl $可以是liisemorpheply lian lian lian lian lian frian a trian frian frian fra a trian fra a trian fra a trian fra a trian fra a trian fra（这是其他作者早期研究的。
Let $\mathbb K$ be a field of characteristic zero, $A$ an integral domain over $\mathbb K$ with the field of fractions $R = \text{Frac}(A),$ and $\text{Der}_{\mathbb{K}}A$ the Lie algebra of all $\mathbb K$-derivations on $A$. Let $W(A):=R\text{Der}_{\mathbb{K}} A$ and $L$ a nilpotent subalgebra of rank $n$ over $R$ of the Lie algebra $W(A).$ We prove that if the center $Z=Z(L)$ is of rank $\geq n-2$ over $R$ and $F=F(L)$ is the field of constants for $L$ in $R,$ then the Lie algebra $FL$ is contained in a locally nilpotent subalgebra of $ W(A)$ of rank $n$ over $R$ with a natural basis over the field $R.$ It is also also proved that the Lie algebra $FL$ can be isomorphically embedded (as an abstract Lie algebra) into the triangular Lie algebra $u_n(F)$ which was studied early by other authors.
