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.

中文翻译：

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Exel–Pardo C ∗-代数的代数模拟

我们介绍了整数矩阵对A，B的Katsura C ^∗代数的代数形式以及在图上具有自相似作用的Exel–Pardo C ^∗代数的代数形式。我们证明了这类代数的一个等级唯一性定理，并将后者的同态构造成在温和条件下为同构的Steinberg代数。与非Hausdorff群上的Steinberg代数一起使用，我们证明了在单数情况下，我们的Katsura C ^∗-代数的代数形式都与Steinberg代数同构。