Continuous quivers of type A (I) Foundations

2019/09/23 by Igusa, Kiyoshi, Rock, Job D., Todorov, Gordana · 5 citations
#18E30: 16G20 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1909.10499

Abstract

We generalize type A quivers to continuous type A quivers and prove initial results about pointwise finite-dimensional (pwf) representations. We classify the indecomosable pwf representations and provide a decomposition theorem, recovering results of Botnan and Crawley-Boevey. We also classify the indecomposable pwf projective representations. Finally, we prove that many of the properties of finite-dimensional type A_n representations are present in finitely generated pwf representations. This is the self-contained foundational part of a series of works to study a generalization of continuous clusters categories and their relationship to other type A cluster structures.

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