Endomorphisms of Lie groups over local fields
Abstract
Lie groups over local fields furnish prime examples of totally disconnected, locally compact groups. We discuss the scale, tidy subgroups and further subgroups (like contraction subgroups) for analytic endomorphisms of such groups. The text is both a research article and a worked out set of lecture notes for a mini-course held June 27-July 1, 2016 at the MATRIX research center in Creswick (Australia) as part of the "Winter of Disconnectedness". The text can be read in parallel to the earlier lecture notes arXiv:0804.2234 which are devoted to automorphisms, with sketches of proof. Complementary aspects are emphasized.
Cite
@article{arxiv.1701.01804,
title = {Endomorphisms of Lie groups over local fields},
author = {Helge Glockner},
journal= {arXiv preprint arXiv:1701.01804},
year = {2017}
}
Comments
Former titles were "Scale functions on Lie groups over local fields of positive characteristic", "Automorphisms of Lie groups over local fields of positive characteristic", "Automorphisms of Lie groups over local fields and related invariant manifolds" and "Lie groups of type R over local fields of positive characteristic". C^k-Lie groups may be treated in a later work. v2: 76 pages