论文标题
正式地图的中央器
Centralisers of formal maps
论文作者
论文摘要
我们考虑在任何有限的尺寸$ d $中具有正式地图，并在具有身份的整体域$ k $中具有系数。那些在正式构图下可逆的形式形式的$ \ mathcal {g} $。我们考虑\ Mathcal {g} $的元素$ g \的centraliser $ c_g $，该元素与$ \ Mathcal {g} $的身份相切。有限订单的要素总是具有无数的centerisiser。如果$ g $具有无限订单，而$ k $是特征零字段，我们表明$ c_g $包含添加剂$（k，+）$的同构副本。如果$ g $具有无限的订单，并且$ k $具有有限的特征，我们表明$ c_g $包含一个无数的Abelian子组。 证明在有限特征和特征零中完全不同，但通过所谓的总和函数连接。
We consider formal maps in any finite dimension $d$ with coefficients in an integral domain $K$ with identity. Those invertible under formal composition form a group $\mathcal{G}$. We consider the centraliser $C_g$ of an element $g\in\mathcal{G}$ which is tangent to the identity of $\mathcal{G}$. Elements of finite order always have an uncountable centraliser. If $g$ has infinite order and $K$ is a field of characteristic zero we show that $C_g$ contains an isomorphic copy of the additive group $(K,+)$. If $g$ has infinite order and $K$ has finite characteristic we show that $C_g$ contains an uncountable abelian subgroup. The proofs are quite different in finite characteristic and in characteristic zero, but are connected by so-called sum functions.
