An Algebraic Analogue of Exel–Pardo C∗-Algebras

Authors

Roozbeh Hazrat
David Pask, University of WollongongFollow
Adam Sierakowski, University of WollongongFollow
Aidan Sims, University of WollongongFollow

RIS ID

144108

Publication Details

Hazrat, R., Pask, D., Sierakowski, A. & Sims, A. (2020). An Algebraic Analogue of Exel–Pardo C∗-Algebras. Algebras and Representation Theory,

Abstract

© 2020, Springer Nature B.V. We introduce an algebraic version of the Katsura C∗-algebra of a pair A,B of integer matrices and an algebraic version of the Exel–Pardo C∗-algebra of a self-similar action on a graph. We prove a Graded Uniqueness Theorem for such algebras and construct a homomorphism of the latter into a Steinberg algebra that, under mild conditions, is an isomorphism. Working with Steinberg algebras over non-Hausdorff groupoids we prove that in the unital case, our algebraic version of Katsura C∗-algebras are all isomorphic to Steinberg algebras.