An Algebraic Analogue of Exel–Pardo C -Algebras

Roozbeh Hazrat, David Pask, Adam Sierakowski, Aidan Sims

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)877-909
Number of pages33
JournalAlgebras and Representation Theory
Volume24
Issue number4
DOIs
Publication statusPublished - Aug 2021

Bibliographical note

Publisher Copyright:
© 2020, Springer Nature B.V.

Keywords

  • algebra
  • groupoids
  • matrices

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