This monograph is devoted to a new class of non-commutative rings, skew Poincaré–Birkhoff–Witt (PBW) extensions. Beginning with the basic definitions and ring-module theoretic/homological properties, it goes on to investigate finitely generated …
This paper establishes a link between the theory of cluster algebras and the theory of representations of partially ordered sets. We introduce a class of posets by requiring avoidance of certain types of peak-subposets and show that these posets can …
In this contribution, we study the relationship between the CMV block matrices associated with two symmetric positive definite matrix measures supported on the unit circle. We also consider certain transformations of an orthogonality matrix measure …
Este articulo propone y resuelve un modelo matemático para predecir el comportamiento de la precipitación en la ciudad de Tunja. Para esto, la información pluviométrica se sometió a pruebas de ajuste a funciones de distribución de probabilidad, …
Let 𝜎 be a Hermitian matrix measure supported on the unit circle. In this contribution, we study some algebraic and analytic properties of the orthogonal matrix polynomials associated with the Christoffel matrix transformation of 𝜎 defined by …
In this paper, we introduce weak (Σ,Δ)-compatible rings and study skew Poincaré–Birkhoff–Witt extensions over these rings. We characterize the weak notion of compatibility for several noncommutative rings appearing in noncommutative algebraic …
Given a perturbation of a matrix measure supported on the unit circle, we analyze the perturbation obtained on the corresponding matrix measure on the real line, when both measures are related through the Szegő matrix transformation. Moreover, using …
El propósito de la investigación denominada “La cognición y la enseñanza del concepto de diferencial, desde la teoría APOE. Un aporte a la formación de profesores en matemáticas”, es describir y explicar la forma en que los estudiantes de pregrado comprenden la diferencial de una función en varias variables, que es una propiedad de algunas aplicaciones matemáticas con dominio en un subconjunto abierto del de poder ser aproximadas por una transformación lineal en un punto de su dominio.
In this article, we present necessary and sufficient conditions for a graded (trimmed) double Ore extension to be a graded (quasi-commutative) skew PBW extension. Using this fact, we prove that a graded skew PBW extension A=σ(R)⟨x1,x2⟩ of an …
In this paper we present a computational package developed for making computations involved in many homological applications of the Gr"obner theory of skew PBW extensions.