Tidy subgroups for commuting automorphisms of totally disconnected groups: an analogue of simultaneous triangularisation of matrices

dc.creatorWillis, George A.
dc.date2003-02-18
dc.date.accessioned2026-07-07T04:55:21Z
dc.date.available2026-07-07T04:55:21Z
dc.descriptionLet αbe an automorphism of the totally disconnected group G. The compact open subgroup, V, if G is tidy for αif [α(V') : α(V')\cap V'] is minimised at V, where V' ranges over all compact open subgroups of G. Identifying a subgroup tidy for αis analogous to identifying a basis which puts a linear transformation into Jordan canonical form. This analogy is developed here by showing that commuting automorphisms have a common tidy subgroup of G and, conversely, that a group H of automorphisms having a common tidy subgroup V is abelian modulo the automorphisms which leave V invariant. Certain subgroups of G are the analogues of eigenspaces and corresponding real characters of H the analogues of eigenvalues.
dc.description36 pages, submitted keywords: locally compact group, scale function, tidy subgroup, modular function, automorphism
dc.identifierhttps://arxiv.org/abs/math/0302201
dc.identifierhttp://arxiv.org/abs/math/0302201
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/66549
dc.subjectGroup Theory
dc.subject22D05 (Primary); 22D45, 20E25, 20E36 (Secondary)
dc.titleTidy subgroups for commuting automorphisms of totally disconnected groups: an analogue of simultaneous triangularisation of matrices
dc.typetext

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