En este trabajo se realiza una aproximación crítica, en términos de las implicaciones socioespaciales de carácter nacional y local, a los proyectos e iniciativas de conexión física supranacional mediante el mejoramiento de la infraestructura en transporte y energía. Para ello, se analiza la forma en que los proyectos de infraestructura de Colombia se articulan con dos iniciativas subcontinentales que pretenden construir una plataforma física para la región: el Plan Puebla Panamá (PPP), para Centroamérica (incluida Colombia) y la Iniciativa para la Integración Regional de Suramérica (IIRSA).
Prompted by an inquiry of Manin on whether a coacting Hopf-type structure [Formula: see text] and an algebra [Formula: see text] that is coacted upon share algebraic properties, we study the particular case of [Formula: see text] being a path algebra [Formula: see text] of a finite quiver [Formula: see text] and [Formula: see text] being Hayashi’s face algebra [Formula: see text] attached to [Formula: see text]. This is motivated by the work of Huang, Wicks, Won and the second author, where it was established that the weak bialgebra coacting universally on [Formula: see text] (either from the left, right, or both sides compatibly) is [Formula: see text]. For our study, we define the Kronecker square [Formula: see text] of [Formula: see text], and show that [Formula: see text] as unital graded algebras. Then we obtain ring-theoretic and homological properties of [Formula: see text] in terms of graph-theoretic properties of [Formula: see text] by way of [Formula: see text].
In this paper, our objects of interest are Hopf Galois extensions (e.g., Hopf algebras, Galois field extensions, strongly graded algebras, crossed products, principal bundles, etc.) and families of noncommutative rings (e.g., skew polynomial rings, PBW extensions and skew PBW extensions, etc.) We collect and systematize questions, problems, properties and recent advances in both theories by explicitly developing examples and doing calculations that are usually omitted in the literature. In particular, for Hopf Galois extensions we consider approaches from the point of view of quantum torsors (also known as quantum heaps) and Hopf Galois systems, while for some families of noncommutative rings we present advances in the characterization of ring-theoretic and homological properties. Every developed topic is exemplified with abundant references to classic and current works, so this paper serves as a survey for those interested in either of the two theories. Throughout, interactions between both are presented.
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