论文标题
具有天然分级丝状nilraidal的可溶解谎言谎言的扩展
Extensions of solvable Lie algebras with naturally graded filiform nilradical
论文作者
论文摘要
在这项工作中，我们考虑了与天然分级的丝状nilradicals的可溶性谎言代数的扩展。请注意，存在两个天然分级的丝状谎言代数$ n_ {n，1} $和$ q_ {2n}。$我们找到了代数$ n_ {n，1} $的所有一维中心扩展，并显示$ q_ {2n} $的任何扩展。之后，我们发现可溶解的一维扩展名用nilradical $ n_ {n，1} $。我们证明，有一个唯一的非分类中心扩展，可解决的lie代数，带有nilradical $ n_ {n，1} $的最大编码。此外，所有可解决的谎言代数的一维扩展与nilradical $ n_ {n，1} $相同，其编纂等于一个，并将这些可解的代数与nilradicals与nilradicals进行比较是Algebra $ n_ $ n_ n _ n _ n，1} $的一维中心。
In this work we consider extensions of solvable Lie algebras with naturally graded filiform nilradicals. Note that there exist two naturally graded filiform Lie algebras $n_{n, 1}$ and $Q_{2n}.$ We find all one-dimensional central extensions of the algebra $n_{n, 1}$ and show that any extension of $Q_{2n}$ is split. After that we find one-dimensional extensions of solvable Lie algebras with nilradical $n_{n, 1}$. We prove that there exists a unique non-split central extension of solvable Lie algebras with nilradical $n_{n, 1}$ of maximal codimension. Moreover, all one-dimensional extensions of solvable Lie algebras with nilradical $n_{n, 1}$ whose codimension is equal to one are found and compared these solvable algebras with the solvable algebras with nilradicals are one-dimensional central extension of algebra $n_{n, 1}$.
