March 27
Michał Szachniewicz,
Institute for Advanced Study and Harvard University
Ehrenfeucht–Fraïssé games on classifiable C*-algebras
This talk is based on a joint work with Jennifer Pi and Mira Tartarotti. One of the major goals of operator theory is to classify (a large class of) closed *-algebras of bounded operators on Hilbert spaces, i.e., to classify C*-algebras. In 1976 Elliott proved that a class of AF algebras can be classified by their ordered K-theory. This theorem was generalised to a bigger class of C*-algebras, called classifiable. We prove that there is a transfer of strategies between Ehrenfeucht-Fraïssé games (of various lengths) on classifiable C*-algebras and their invariants consisting of K-theory and traces answering a question from a work of Ben De Bondt, Andrea Vaccaro, Boban Velickovic and Alessandro Vignati.