论文标题
紧凑型群体和（受限）代数的天生和内在性
Naturality and innerness for morphisms of compact groups and (restricted) Lie algebras
论文作者
论文摘要
对于任何（限制）$ l'$的延长派生（内态），对于任何（限制的）谎言形态$ f：l \ t to l'，在明显意义上在$ f $中起作用。我们表明，（a）限制性谎言代数的唯一扩展的内态性是两个明显的内态，将$ l'$的身份或零映射分配给每个$ f $; （b）如果$ l $是特征零的谎言代数或具有积极特征的有限的谎言代数，则$ l $具有典型的射击，其扩展派生的空间（因此，从某种意义上说，后者都是内在的）。这些结果回答了G. Bergman的许多问题。 同样，我们表明，紧凑型组的扩展内态内态性的各个组成部分都是琐碎的或所有内部的自动形态。
An extended derivation (endomorphism) of a (restricted) Lie algebra $L$ is an assignment of a derivation (respectively) of $L'$ for any (restricted) Lie morphism $f:L\to L'$, functorial in $f$ in the obvious sense. We show that (a) the only extended endomorphisms of a restricted Lie algebra are the two obvious ones, assigning either the identity or the zero map of $L'$ to every $f$; and (b) if $L$ is a Lie algebra in characteristic zero or a restricted Lie algebra in positive characteristic, then $L$ is in canonical bijection with its space of extended derivations (so the latter are all, in a sense, inner). These results answer a number of questions of G. Bergman. In a similar vein, we show that the individual components of an extended endomorphism of a compact connected group are either all trivial or all inner automorphisms.
