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An algebraic analogue of Exel-Pardo C*-algebras

Authors :
Hazrat, Roozbeh
Pask, David
Sierakowski, Adam
Sims, Aidan
Publication Year :
2019

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.<br />Comment: 38 pages, 3 figures

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.1912.12117
Document Type :
Working Paper