2004/06/30 by Valentin Deaconu, Deaconu, Valentin · 1 citation
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Holomorphic and Operator Theory #math.OA #msc:46L55
paper · pdf · doi:10.48550/arxiv.math/0406624
10 pages
arxiv created 2004/06/30 · arxiv updated 2009/12/01
Given a compact space X and two commuting continuous open surjective maps sigma1, sigma2 : X --> X, we construct certain C*-algebras that reflect the dynamics of the N2-action. When the maps sigma1, sigma2 are local homeomorphisms, these are groupoid algebras, but in general, we will use a Cuntz-Pimsner algebra associated to a product system of Hilbert bimodules in the sense of Fowler. The motivating example for our construction is the dynamical system associated with a rank two graph by Kumjian and Pask. We consider also a two-dimensional subshift of Ledrappier, the case of two covering maps of the circle, and the two-dimensional Bernoulli shift.