论文标题
在本地急剧的N传递组上
On local sharply n-transitive groups
论文作者
论文摘要
该论文致力于拓扑组对流形的行动的概括。我们考虑一个本地拓扑组，而不是拓扑群体，它概括了拓扑组中A〜胚芽的概念或一个〜社区的概念。引入了本地群体在拓扑空间的行动的概念。 该论文构建了本地$ n $ thansitive群体和本地$ n $ -pseudofields的理论。局部急剧$ n $ n $的群体被简化为简单的代数对象 - 本地$ n $ -n $ -pseudofields，类似于将Lie群体减少到Lie代数的方式，而急剧的两传递组则减少到近域。这可能很有用，因为与本地紧凑型和连接的急剧连接相反，$ n $ n $ n $ n> 3 $不存在，因此，对于任何$ n $，local prinper $ n $ thum-n $ thermantitive组都存在，例如，$ gl_n（\ mathbb {r}）$ n $。所考虑的群体也是有限$ n $ n $ n $的，这也是谎言组，这为他们的研究提供了额外的方法。
The paper is devoted to generalizations of actions of topological groups on manifolds. Instead of a topological group, we consider a local topological group generalizing the notion of a~germ or a~neighborhood in a topological group. The notion of an action of a local group on a topological space is introduced. The paper constructs the theory of local sharply $n$-transitive groups and local $n$-pseudofields. Local sharply $n$-transitive groups are reduced to simpler algebraic objects -- local $n$-pseudofields, similarly to the way Lie groups are reduced to Lie algebras, and sharply two-transitive groups, are reduced to neardomains. This can be useful, since, opposite to locally compact and connected sharply $n$-transitive groups, which are absent for $n > 3$, local sharply $n$-transitive groups exist for any $n$, for example, the group $GL_n(\mathbb{R})$. Being boundedly sharply $n$-transitive, the groups under consideration are also Lie groups, which gives extra methods for their study.
