Mathematics – Group Theory
Scientific paper
2006-10-30
Mathematics
Group Theory
20 pages, LaTeX
Scientific paper
To each totally disconnected, locally compact topological group G and each group A of automorphisms of G, a pseudo-metric space of ``directions'' has been associated by U. Baumgartner and the second author. Given a Lie group G over a local field, it is a natural idea to try to define a map from the space of directions of analytic automorphisms of G to the space of directions of automorphisms of the Lie algebra L(G) of G, which takes the direction of an analytic automorphism of G to the direction of the associated Lie algebra automorphism. We show that, in general, this map is not well-defined. However, the pathology cannot occur for a large class of linear algebraic groups (called ``generalized Cayley groups'' here). For such groups, the assignment just proposed defines a well-defined isometric embedding from the space of directions of inner automorphisms of G to the space of directions of automorphisms of L(G). Some counterexamples concerning the existence of small joint tidy subgroups for flat groups of automorphisms are also provided.
Glockner Helge
Willis George A.
No associations
LandOfFree
Directions of automorphisms of Lie groups over local fields compared to the directions of Lie algebra automorphisms does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Directions of automorphisms of Lie groups over local fields compared to the directions of Lie algebra automorphisms, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Directions of automorphisms of Lie groups over local fields compared to the directions of Lie algebra automorphisms will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-231198