Algebraically equipped posets

2015/01/13 by R. Bautista, Bautista, Raymundo, Ivon Dorado +1
Mathematics · Physics and Astronomy · #06A11 #16G20 #16G60 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1501.03074

openalex publication_date 2015/01/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce partially ordered sets (posets) with an additional structure given by a collection of vector subspaces of an algebra A. We call them algebraically equipped posets. Some particular cases of these, are generalized equipped posets and p-equipped posets, for a prime number p. We study their categories of representations and establish equivalences with some module categories, categories of morphisms and a subcategory of representations of a differential tensor algebra. Through this, we obtain matrix representations and its corresponding matrix classification problem.

Related

• Generating naturally labeled posets through matrix extensions, order ideals and automorphism groups
• Representations and corepresentations of p-equipped posets
• A geometric realization of socle-projective categories for posets of type \mathbbA
• Topological Representations of Posets
• Algebras describing pseudocomplemented, relatively pseudocomplemented and sectionally pseudocomplemented posets