The socle and semisimplicity of a Kumjian-Pask algebra

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.

References in corpus (4)

• Periodicity in Rank 2 Graph Algebras
• Kumjian-Pask algebras of higher-rank graphs
• Entropy of shifts on higher-rank graph C*-algebras
• When is the Cuntz-Krieger algebra of a higher-rank graph approximately finite-dimensional?