Directions of automorphisms of Lie groups over local fields compared to the directions of Lie algebra automorphisms

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dc.creatorGlockner, Helge
dc.creatorWillis, George A.
dc.date2006-10-30
dc.date.accessioned2026-07-07T07:29:38Z
dc.date.available2026-07-07T07:29:38Z
dc.descriptionTo 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.
dc.description20 pages, LaTeX
dc.identifierhttps://arxiv.org/abs/math/0610944
dc.identifierhttp://arxiv.org/abs/math/0610944
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/118189
dc.subjectGroup Theory
dc.subject22D05 (primary) 20G25; 22D45; 22E15; 22E35 (secondary)
dc.titleDirections of automorphisms of Lie groups over local fields compared to the directions of Lie algebra automorphisms
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