Simple modules for Kumjian-Pask algebras
Raimund Preusser

TL;DR
This paper develops a framework for modules over Kumjian-Pask algebras using representation k-graphs, characterizes simple modules, and explores their categorical structure via higher-rank graph coverings.
Contribution
It introduces the concept of representation k-graphs for higher-rank graphs and characterizes which yield simple modules for Kumjian-Pask algebras.
Findings
Representation k-graphs produce modules for Kumjian-Pask algebras.
Simple modules are characterized via representation k-graphs.
The category of representation k-graphs is analyzed using higher-rank graph coverings.
Abstract
The paper introduces the notion of a representation -graph for a given -graph . It is shown that any representation -graph for yields a module for the Kumjian-Pask algebra , and the representation -graphs yielding simple modules are characterised. Moreover, the category of representation -graphs for is investigated using the covering theory of higher-rank graphs.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Rings, Modules, and Algebras · Advanced Topics in Algebra
