Work

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

Year: 2025

Type: article

Abstract: In this article, we provide a description of the Auslander–Reiten quiver for certain posets endowed with an involution, which we denote as types $$\mathfrak {U}_n$$ U n and $$\mathfrak {U}_\infty $$ U ∞ . These posets appear in Zavadskij’s Differentiation III (Can Math Soc Conf Proc 11:299–323, 1991). Our approach follows the classical Auslander–Reiten theory developed by Auslander, Reiten, and Smalø (Representation Theory of Artin Algebras. Cambridge Studies in Advanced Mathematics, UK, 1992). To this end, we establish a natural exact structure for the category of representations of a partially ordered set with an involution, and subsequently delineate the projective and injective representations.

Source: Boletín de la Sociedad Matemática Mexicana

DOI: 10.1007/s40590-025-00735-7

Authors: Raymundo Bautista, Verónica Cifuentes

Institutions: Centro de Ciencias Matemáticas, Universidad Nacional Autónoma de México, Universidad Distrital Francisco José de Caldas

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

OpenAlex ID: W4409187469