collaborators

5 papers

math.OA2025

Twisted operator algebras of self-similar groupoid actions on arbitrary graphs

B. K. Kwaśniewski, A. Mundey

We study self-similar groupoid actions on arbitrary directed graphs together with -valued twists that exhaust the second cohomology group of the associated Zappa-Szép…

math.OA2025

Self-similar groupoid actions on k-graphs, and invariance of K-theory for cocycle homotopies

Alexander Mundey, Aidan Sims

We establish conditions under which an inclusion of finitely aligned left-cancellative small categories induces inclusions of twisted C*-algebras. We also present an example of an…

math.OA2025

Splittings for C*-correspondences and strong shift equivalence

Kevin Aguyar Brix, Alexander Mundey, Adam Rennie

We present an extension of the notion of in-splits from symbolic dynamics to topological graphs and, more generally, to C*-correspondences. We demonstrate that in-splits provide ex…

math.KT2024

Homology and twisted C*-algebras for self-similar actions and Zappa-Szép products

Alexander Mundey, Aidan Sims

We study the categorical homology of Zappa-Szép products of small categories, which include all self-similar actions. We prove that the categorical homology coincides with the hom…

math.OA2024

Morphisms of Cuntz-Pimsner algebras from completely positive maps

Kevin Aguyar Brix, Alexander Mundey, Adam Rennie

We introduce positive correspondences as right C*-modules with left actions given by completely positive maps. Positive correspondences form a semi-category that contains the C*-co…