论文标题
非lie子群体中的谎言群体上的局部特征的本地领域
Non-Lie subgroups in Lie groups over local fields of positive characteristic
论文作者
论文摘要
根据Cartan的定理，每个封闭的子组$ h $的真实（或$ p $ -ADIC）lie Group $ g $都是谎言子组。对于积极特征的本地字段$ {\ mathbb k} $的谎言组，众所周知，类似的结论是错误的。我们展示了更多：存在$ {\ mathbb k} $ - 分析谎言组$ g $和一个非污染的，紧凑的亚组$ h $，以至于每$ {\ mathbb k} $ - 分析歧管$ m $，每个$ {\ mathbb k} $ f \ colon m $ is $ f $ f $ f $ f $ f（mathbb k} $ f $ f（mathbb k} $ f $ f $ \ f $ \ f（mathers collys f $ f（mathert collys s $ f（mathers collys f of）特别是，集合$ h $不接受非discrete $ {\ mathbb k} $ - 分析歧管结构，该结构将$ h $包含在$ g $ a $ a $ a $ {\ mathbb k} $ - 分析图中。此外，我们可以实现这一目标，$ h $不承认$ {\ mathbb k} $ - 分析谎言组结构与$ h $上的$ g $构成的拓扑组结构兼容。
By Cartan's Theorem, every closed subgroup $H$ of a real (or $p$-adic) Lie group $G$ is a Lie subgroup. For Lie groups over a local field ${\mathbb K}$ of positive characteristic, the analogous conclusion is known to be wrong. We show more: There exists a ${\mathbb K}$-analytic Lie group $G$ and a non-discrete, compact subgroup $H$ such that, for every ${\mathbb K}$-analytic manifold $M$, every ${\mathbb K}$-analytic map $f\colon M\to G$ with $f(M)\subseteq H$ is locally constant. In particular, the set $H$ does not admit a non-discrete ${\mathbb K}$-analytic manifold structure which makes the inclusion of $H$ into $G$ a ${\mathbb K}$-analytic map. We can achieve that, moreover, $H$ does not admit a ${\mathbb K}$-analytic Lie group structure compatible with the topological group structure induced by $G$ on $H$.
