Andrea Vaccaro "Games on Approximately Finite C*-algebras"

jeudi 9 déc. 2021, 11:00 → 12:00 Europe/Paris

Fokko (Braconnier)

Games on Approximately Finite C*-algebras

By a well-known classification result in operator algebras due to George Elliott, the isomorphism class of an approximately finite C*-algebra (or simply AF-algebra) is completely determined by its dimension group. The latter is a C*-algebraic invariant which (for separable C*-algebras) takes the form of an (countable) ordered abelian group. The main result
of my talk is model theoretic version of Elliott's result in the context of infinitary logic. In particular, Elliott's arguments can be combined with a metric version of the dynamic Ehrenfeucht–Fraïssé game to show that elementary equivalence up to a rank alpha between AF-algebras is
verified if elementary equivalence, up to a rank only depending on alpha, between the corresponding dimension groups holds. I will also show how this result can be used to build a class of simple AF-algebras of arbitrarily high Scott Rank.