MF Actions and K-theoretic Dynamics

2014/04/16 by Timothy Rainone, Rainone, Timothy
Mathematics · #46L05 #46L55 #FOS: Mathematics #Operator Algebras (math.OA) #math.OA #msc:46L05 #msc:46L55

paper · pdf · doi:10.48550/arxiv.1404.4389

To appear in J. Funct. Anal. 30 pages

arxiv created 2014/04/16 · arxiv updated 2014/04/18

Abstract

We study the interplay of C*-dynamics and K-theory. Notions of chain recurrence for transformations groups (X,G) and MF actions for non-commutative C*-dynamical systems (A,G) are translated into K-theoretical language, where purely algebraic conditions are shown to be necessary and sufficient for a reduced crossed product to admit norm microstates. We are particularly interested in actions of free groups on AF algebras, in which case we prove that a K-theoretic coboundary condition determines whether or not the reduced crossed product is a Matricial Field (MF) algebra. One upshot is the equivalence of stable finiteness and being MF for these reduced crossed product algebras.

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