11 papers
An Algebraic View of Amenable Groupoids
Karol Herrera, Andrés Rubiano
We introduce source-anchored algebraic amenability for Hausdorff ample groupoids, a Følner condition formulated in the Steinberg algebra and localized at compact open subsets of th…
Normal Ordering and Stirling-Type Combinatorics for Double Ore Extensions of Type (14641)
Andrés Rubiano
We develop an explicit PBW normal ordering theory for the double extension regular algebras of type in the Zhang-Zhang classification. With respect to the order $x_1…
Combinatorial aspects of normal ordering of 3-dimensional skew polynomial rings
Andrés Rubiano, Armando Reyes
In this paper, we discuss combinatorial aspects of normal ordering of 3-dimensional skew polynomial rings defined and classified by Bell and Smith \cite{BellSmith1990}. With some h…
Noncommutative differential geometry of ambiskew polynomial rings
Andrés Rubiano, Armando Reyes
We determine sufficient criteria for the differential smoothness of ambiskew polynomial rings defined and studied by D. A. Jordan in several papers \cite{FishJordan2019, Jordan1993…
A note on explicit homological invariants of graded double Ore extensions
Andrés Rubiano
We compute explicit homological invariants of a trimmed graded double Ore extension of the quantum plane. For a pilot family of type (14641), we determine the minimal graded free r…
On the smoothness of 3-dimensional skew polynomial rings
Andrés Rubiano, Armando Reyes
This paper is part of a series of papers in which we have investigated the differential smoothness of families of noncommutative algebras. Here, we consider this topic for the fami…
Center of double extension regular algebras of type (14641)
Andrés Rubiano
In this paper we compute the center and, in several cases, central subalgebras of double Ore extensions of type (14641) under suitable restrictions on the defining parameters. Part…
On the annihilator condition for skew PBW extensions
Karol Herrera, Sebastián Higuera, Andrés Rubiano
We investigate the annihilator condition for skew Poincaré-Birkhoff-Witt extensions. We prove that some results about the annihilator condition for skew polynomia…
Finite Gröbner-Shirshov bases for double extension regular algebras of type (14641)
Karol Herrera, Sebastián Higuera, Andrés Rubiano
In this paper, we compute the Gröbner-Shirshov bases for certain regular double extension algebras by means of an algorithm implemented in Matlab, which facilitates the underlying…
A view toward the smooth geometry of Sklyanin algebras
Karol Herrera, Sebastián Higuera, Andrés Rubiano
We study the differential smoothness of Sklyanin algebras in three and four variables. We show that all non-degenerate three-dimensional cases are differentially smooth, while none…
On differential smoothness of certain Artin-Schelter regular algebras of dimension 5
Andrés Rubiano
This article investigates the differential smoothness of various five-dimensional Artin-Schelter regular algebras. By analyzing the relationship between the number of generators an…