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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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