Adam Dor-On, Department of Pure Mathematics, University of Waterloo
“Cuntz-Pimsner algebras and Subproduct Systems arising from Stochastic Matrices”
Arveson-Stinespring subproduct systems, introduced by Shalit and Solel in their paper “Subproduct systems”, are invariants of non-commutative dynamics used in their classification and dilation theory. We study Arveson-Stinespring subproduct systems arising from stochastic matrices. The computation of these subproduct systems tells us exactly when two stochastic matrices have (unitarily) isomorphic subproduct systems in terms of the matrices. This characterization then leads to show that recurrent stochastic matrices are completely distinguished by their associated subproduct systems. Moving on a slightly different path, we compute the generalized Cuntz-Pimsner algebra (in the sense of Viselter) associated to a (subproduct system of) finite recurrent stochastic matrices and see what information can be retrieved on the matrix from the algebra.
This work is part of a soon-to-appear joint paper with Daniel Markiewicz.