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An algebraic analogue of Exel-Pardo C*-algebras
- 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
- Subjects :
- Mathematics - Rings and Algebras
Mathematics - Operator Algebras
16D70, 16W50
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1912.12117
- Document Type :
- Working Paper