Tuesday, December 5, 2017
The Fraisse Limit of Finite Dimensional Matrix Algebras with the Rank Metric
Aaron Anderson, Caltech
We show that a certain ring, constructed by von Neumann and realized as the coordinatization of a continuous geometry, can also be realized as the metric Fra ı̈ssé limit of the class of finite-dimensional matrix algebras over a field of scalars, equipped with the rank metric. We show that the automorphism group of this metric structure is extremely amenable,implying (by the metric Kechris-Pestov-Todorcevic correspondence) an approximate Ramsey Property, which is also proved directly.