Algebraically equipped posets
Raymundo Bautista, Ivon Dorado

TL;DR
This paper introduces algebraically equipped posets, a new structure combining posets with algebraic subspace data, and explores their representation theory, including matrix classification.
Contribution
It defines algebraically equipped posets and establishes their equivalences with module categories and differential tensor algebra representations, providing new tools for their analysis.
Findings
Established equivalences with module categories
Developed matrix representations and classification methods
Connected algebraically equipped posets to differential tensor algebra
Abstract
We introduce partially ordered sets (posets) with an additional structure given by a collection of vector subspaces of an algebra . We call them algebraically equipped posets. Some particular cases of these, are generalized equipped posets and -equipped posets, for a prime number . 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.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Nonlinear Waves and Solitons
