Adam Dor On, Technion
"Cuntz-Nica-Pimsner algebras over $\mathbb{N}^d$"
An effective model for encoding multivariable dynamical systems via C*-algebras is given by Toeplitz-Nica-Pimsner algebras introduced by Fowler. In the work of Carlsen, Larsen, Sims and Vitadello, the right notion of a "boundary quotient" Cuntz-Nica-Pimsner algebra is established, but the precise relations between minimal generators are sometimes very difficult to ascertain.
In joint work with Evgenios Kakariadis we introduce a new class of product systems over $\mathbb{N}^d$ that yield tractable relations for associated Cuntz-Nica-Pimsner algebras in terms of the coefficient algebra. Our approach provides a unified treatment for exactness, nuclearity and relative CNP algebra results in the literature. We showcase our new relations in concrete examples such as C*-dynamical systems as investigated by Davidson, Fuller and Kakariadis, and finitely aligned higher-rank graphs as studied by Raeburn, Sims and Yeend.
MC 5479