Markovianity and the Thompson Monoid F^+
Arundhathi Krishnan (University College Cork)
Thursday 1st October, 2020 16:00-17:00 Contact one of the organizers for Zoom coordinates
In the process of identifying a suitable distributional symmetry to describe Markovianity, it has been conjectured by C. Köstler that there is a certain correspondence between unilateral Markov shifts and representations of the Thompson monoid F^+.
After having illustrated this correspondence in the context of tensor products of W*-algebraic probability spaces, I will present the following two general results. A representation of the Thompson monoid F^+ in the endomorphisms of a W*-algebraic probability space yields a noncommutative Markov process (in the sense of Kümmerer). Conversely, such a representation is obtained from a noncommutative Markov process which is given as a coupling to a so-called spreadable noncommutative Bernoulli shift.
This is joint work with Claus Köstler and Stephen Wills.