- Title
- Directions of automorphisms of lie groups over local fields compared to the directions of lie algebra automorphisms
- Creator
- Glöckner, Helge; Willis, George A.
- Relation
- 22nd Summer Conference on Topology and its Applications. Proceedings of the 22nd Summer Conference on Topology and its Applications [presented in Topology Proceedings, Vol. 31, No. 2] (Castellón, France 24-27 July, 2007) p. 481-501
- Relation
- http://www.topology.auburn.edu/tp/reprints/v31/r2.htm
- Publisher
- Auburn University
- Resource Type
- conference paper
- Date
- 2007
- Description
- 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.
- Subject
- group algebras; Lie algebra; automorphisms; generalized Cayley groups
- Identifier
- http://hdl.handle.net/1959.13/933600
- Identifier
- uon:11666
- Identifier
- ISSN:0146-4124
- Language
- eng
- Full Text
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