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arXiv · 1912.12117

An algebraic analogue of Exel-Pardo C*-algebras

Roozbeh Hazrat·David Pask·Adam Sierakowski·Aidan Sims
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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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Roozbeh Hazrat, David Pask, Adam Sierakowski, Aidan Sims. 2019-12-27. An algebraic analogue of Exel-Pardo C*-algebras. https://arxiv.org/abs/1912.12117

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