Graduate Geometry, Topology and Dynamics Seminar
Kitty Yang
Northwestern University
Normal amenable subgroups of automorphism groups of shifts of finite type
Abstract: Given any shift system, the center of the automorphism group contains the subgroup generated by the shift map, and for shifts of finite type, the center is precisely the subgroup generated by the shift, which is due to Ryan. We generalize Ryan's Theorem to show that any normal amenable subgroup of the automorphism group of a mixing shift of finite type is contained in the subgroup generated by the shift maps. We also show that the result does not extend to higher dimensions by giving an example of a two-dimensional mixing shift of finite type whose automorphism group is amenable and not generated by the shift maps.
Wednesday October 3, 2018 at 4:00 PM in 612 SEO