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arXiv · 2105.07265

Simple modules for Kumjian-Pask algebras

Raimund Preusser
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Abstract

The paper introduces the notion of a representation $k$-graph $(\Delta,\alpha)$ for a given $k$-graph $\Lambda$. It is shown that any representation $k$-graph for $\Lambda$ yields a module for the Kumjian-Pask algebra $KP(\Lambda)$, and the representation $k$-graphs yielding simple modules are characterised. Moreover, the category $RG(\Lambda)$ of representation $k$-graphs for $\Lambda$ is investigated using the covering theory of higher-rank graphs.

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Raimund Preusser. 2021-05-15. Simple modules for Kumjian-Pask algebras. https://arxiv.org/abs/2105.07265

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