Representations of relative Cohn path algebras

2018/06/08 by Canto, Cristóbal Gil, Gonçalves, Daniel · 1 citation
#16G99 #16S99 #FOS: Mathematics #Operator Algebras (math.OA) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1806.03077

Abstract

We study relative Cohn path algebras, also known as Leavitt-Cohn path algebras, and we realize them as partial skew group rings (to do this we prove uniqueness theorems for relative Cohn path algebras). Furthermore, given any graph E we define E-relative branching systems and prove how they induce representations of the associated relative Cohn path algebra. We give necessary and sufficient conditions for faithfulness of the representations associated to E-relative branching systems (this improves previous results known to Leavitt path algebras of row-finite graphs with no sinks). To prove this last result we show first a version, for relative Cohn-path algebras, of the reduction theorem for Leavitt path algebras.

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• Relative ultragraph algebras and infinite interval maps

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