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.
Original language | English |
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Pages (from-to) | 877-909 |
Number of pages | 33 |
Journal | Algebras and Representation Theory |
Volume | 24 |
Issue number | 4 |
DOIs | |
Publication status | Published - Aug 2021 |
Bibliographical note
Publisher Copyright:© 2020, Springer Nature B.V.
Keywords
- algebra
- groupoids
- matrices