论文标题
多项式自动形态组的线性和非线性
Linearity and Nonlinearity of groups of polynomial automorphisms
论文作者
论文摘要
令$ k $为一个字段，让$ \ aut \，k^2 $为$ k^2 $的多项式自动形态。如果$ k $是无限的，则该组是非线性的。此外，当$ \ ch \，k = 0 $时，它包含非线性FG子组。在相反的情况下，它包含一些线性的“有限的编码”子组。这种现象是特定于二维的特定的：也证明，即使对于有限的字段$ k $，$ \ aut \，k^3 $的“有限编码”子组是非线性的。
Let $K$ be a field, and let $\Aut \,K^2$ be the group of polynomial automorphisms of $K^2$. If $K$ is infinite, this group is nonlinear. Moreover it contains nonlinear FG subgroups when $\ch\,K=0$. On the opposite, it contains some linear "finite codimension" subgroups. This phenomenon is specific to dimension two: it is also proved that "finite codimension" subgroups of $\Aut\,K^3$ are nonlinear, even for a finite field $K$.
