Title

An Algebraic Analogue of Exel–Pardo C -Algebras

Publication Name

Algebras and Representation Theory

Abstract

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.

Open Access Status

This publication may be available as open access

Volume

24

Issue

4

First Page

877

Last Page

909

Funding Number

DP150101598

Funding Sponsor

Centre of Excellence for Environmental Decisions, Australian Research Council

Share

COinS
 

Link to publisher version (DOI)

http://dx.doi.org/10.1007/s10468-020-09973-x