局部域上的可收缩李群
Contractible Lie groups over local fields
摘要：
设G是一个正特征局部域上的李群，其中f是压缩自同构（即，每个群元素x的前向迭代f^n（x）收敛到中性元1）。证明了G是有限指数幂零扭群。我们还得到了关于李群在局部域上的压缩自同构、它们的李代数的压缩自同构和正阶化之间的相互作用的结果。有些结果甚至推广到任意完备超度量域上的李群。
英文摘要：
Let G be a Lie group over a local field of positive characteristic which admits a contractive automorphism f (i.e., the forward iterates f^n(x) of each group element x converge to the neutral element 1). We show that then G is a torsion group of finite exponent and nilpotent. We also obtain results concerning the interplay between contractive automorphisms of Lie groups over local fields, contractive automorphisms of their Lie algebras, and positive gradations thereon. Some of the results even extend to Lie groups over arbitrary complete ultrametric fields.
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