An algebraic analogue of Exel-Pardo C*-algebras

2019/12/27 by Hazrat, Roozbeh, Pask, David, Sierakowski, Adam +1 · 1 citation
#16D70 #16W50 #FOS: Mathematics #Operator Algebras (math.OA) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1912.12117

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.

Cited by

• Simplicity of algebras and C^*-algebras of self-similar groupoids

Related

• Exel-Pardo algebras of self-similar k-graphs
• Self-similar graphs, a unified treatment of Katsura and Nekrashevych\n C*-algebras
• Graphs, groups and self-similarity
• Self-similar group actions on ultragraphs and associated C^*-algebras
• Self-Similar k-Graph C*-Algebras