The socle and semisimplicity of a Kumjian-Pask algebra

2012/01/09 by Brown, Jonathan H., Huef, Astrid an · 1 citation
#16D70 #16S10 #16W50 #FOS: Mathematics #Operator Algebras (math.OA) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1201.1888

Abstract

The Kumjian-Pask algebra KP(Λ) is a graded algebra associated to a higher-rank graph Λand is a generalization of the Leavitt path algebra of a directed graph. We analyze the minimal left-ideals of KP(Λ), and identify its socle as a graded ideal by describing its generators in terms of a subset of vertices of the graph. We characterize when KP(Λ) is semisimple, and obtain a complete structure theorem for a semisimple Kumjian-Pask algebra.

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• The Leavitt inverse semigroup of a separated graph

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