多项式自同构群的线性与非线性
Linearity and Nonlinearity of groups of polynomial automorphisms
摘要：
设$K$是一个域，$\Aut \,K^2$是$K^2$的多项式自同构群。如果$K$是无限的，那么这个群是非线性的。而且当$\ch\,K=0$ .相反，它包含一些线性“有限余维”子群。这一现象是二维域所特有的：我们还证明了$\Aut\,K^3$的“有限余维”子群是非线性的，即使对于有限域$K$也是如此.
英文摘要：
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 $K$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
