Contraction groups and scales of automorphisms of totally disconnected locally compact groups

By Udo Baumgartner, George A. Willis. 2003

109 citations recorded by the source corpus.

We study contraction groups for automorphisms of totally disconnected locally compact groups using the scale of the automorphism as a tool. The contraction group is shown to be unbounded when the inverse automorphism has non-trivial scale and this scale is shown to be the inverse value of the modular function on the closure of the contraction group at the automorphism. The closure of the contraction group is represented as acting on a homogenous tree and closed contraction groups are characterised.

Subfields: Mathematical Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/efa0f8c04550d55c5283016d5f88b5c88ab82e7c

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In Mathematical Physics

In Nuclear and High Energy Physics

Citations in the corpus

LOCALLY NORMAL SUBGROUPS OF TOTALLY DISCONNECTED GROUPS. PART II: COMPACTLY GENERATED SIMPLE GROUPS (2014, background): “It follows from results in [59] and [7] that nub(f) is trivial if and only if con(f) is closed.”
Commensurated Subgroups of Arithmetic Groups, Totally Disconnected Groups and Adelic Rigidity (2009, methodology): “ subgroup K(2) α′ , deﬁned in (2). Since K (2) α′ is contained in every subgroup tidy for α′, it is contained in K hα,Ni. (This is the same argument as used to prove one direction of Lemma 3.31(3) in [4].) Proposition 4.5. Let N ⊳H ≤ Aut(G) be as in 4.1(a) and 4.1(b). Then for every ﬁnite set h ⊂ H ”