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SUMMARY:Ville Salo: "Gate lattices and the stabilized automorphism group"
DTSTART:20230510T120000Z
DTEND:20230510T130000Z
DTSTAMP:20260614T163400Z
UID:indico-event-9844@indico.math.cnrs.fr
DESCRIPTION:If G is a residually finite countably infinite group\, and X i
 s a subshift over G\, then we associate to X a large countably infinite di
 screte group\, whose generators are homeomorphisms induced by "reversible 
 logical gates" applied at every element of a finite-index subgroup of G. W
 e call the resulting group L. We show that under two dynamical assumptions
  on X (namely that X is of finite type\, and has a gluing property we call
  EFP)\, the commutator [L\, L] is simple\, and forms the monolith (unique 
 minimal nontrivial normal subgroup) of L.\n\nWe also outline the dynamical
  context for this result: Hartman\, Kra and Schmieding define the stabiliz
 ed automorphism group of a subshift as the union of automorphism groups of
  finite-index subactions. They have shown that for full shifts on integers
 \, the "inert part" of this group is simple. It turns out that this inert 
 part coincides with [L\, L]\, so our result generalizes theirs in several 
 directions.\n\nhttps://indico.math.cnrs.fr/event/9844/
LOCATION:435 (UMPA)
URL:https://indico.math.cnrs.fr/event/9844/
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