On the Auslander-Reiten quiver for the category of representations of partially ordered sets with an involution

In this article we describe the Auslander-Reiten quiver for some posets with an involution, that we call types \(\mathfrak{U}_n\) and \(\mathfrak{U}_\infty\). These posets appear in the differentiation III of Zavadskij [12]. We follow the approach to classical Auslander-Reiten theory due to Auslande...

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Bibliographic Details
Published in:arXiv.org 2022-07
Main Authors: Raymundo Bautista Ramos, Verónica Cifuentes Vargas
Format: Article
Language:English
Subjects:
Representations
Set theory
Online Access:Get full text
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Summary:In this article we describe the Auslander-Reiten quiver for some posets with an involution, that we call types \(\mathfrak{U}_n\) and \(\mathfrak{U}_\infty\). These posets appear in the differentiation III of Zavadskij [12]. We follow the approach to classical Auslander-Reiten theory due to Auslander, Reiten and Smal\o{}[1]. For this purpose, we give a natural exact structure for the category of representations of a partially ordered set with an involution. We describe the projective and injective representations
ISSN:2331-8422