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An Algebraic Analogue of Exel–Pardo C∗-Algebras

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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.

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Authors and Affiliations

  1. School of Computing, Engineering and Mathematics, Western Sydney University, Parramatta, NSW, 2150, Australia

    Roozbeh Hazrat

  2. School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW, 2522, Australia

    David Pask, Adam Sierakowski & Aidan Sims

Authors
  1. Roozbeh Hazrat
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  2. David Pask
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  3. Adam Sierakowski
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  4. Aidan Sims
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Correspondence to Adam Sierakowski.

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Presented by: Kenneth Goodearl

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This research was supported by the Australian Research Council.

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Hazrat, R., Pask, D., Sierakowski, A. et al. An Algebraic Analogue of Exel–Pardo C∗-Algebras. Algebr Represent Theor 24, 877–909 (2021). https://doi.org/10.1007/s10468-020-09973-x

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  • DOI: https://doi.org/10.1007/s10468-020-09973-x

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