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arXiv · 1201.1888

The socle and semisimplicity of a Kumjian-Pask algebra

Jonathan H. Brown·Astrid an Huef
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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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Jonathan H. Brown, Astrid an Huef. 2012-02-01. The socle and semisimplicity of a Kumjian-Pask algebra. https://arxiv.org/abs/1201.1888

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