# An Algebraic Analogue of Exel–Pardo C∗-Algebras

@article{Hazrat2019AnAA,
title={An Algebraic Analogue of Exel–Pardo C∗-Algebras},
journal={Algebras and Representation Theory},
year={2019},
volume={24},
pages={877 - 909}
}
• Published 27 December 2019
• Mathematics
• Algebras and Representation Theory
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…
We introduce the Exel-Pardo ∗-algebra EPR(G,Λ) associated to a self-similar kgraph (G,Λ, φ). We prove the Z-graded and Cuntz-Krieger uniqueness theorems for such algebras and investigate their ideal
• Mathematics
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• 2022
Nekrashevych algebras of self-similar group actions are natural generalizations of the classical Leavitt algebras. They are discrete analogues of the corresponding Nekrashevych $C^\ast$-algebras. In

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