9 papers
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…
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…
Differential smoothness of bi-quadratic algebras with PBW basis
Andrés Rubiano, Armando Reyes
We investigate the differential smoothness of bi-quadratic algebras with PBW basis.
A note on the differential smoothness of skew PBW extensions
Andrés Rubiano, Armando Reyes
We investigate the differential smoothness of a certain family of skew Poincaré-Birkhoff-Witt extensions.
Smooth Geometry of Diffusion Algebras
Andrés Rubiano, Armando Reyes
In this paper, we study the differential smoothness of diffusion algebras.
Smooth geometry of double extension regular algebras of type (14641)
Andrés Rubiano, Armando Reyes
In this paper, we prove that double extension regular algebras of type (14641) are not differentially smooth.
Smooth geometry of skew PBW extensions over commutative polynomial rings I
Andrés Rubiano, Armando Reyes
In this paper, we investigate the differential smoothness of skew PBW extensions over commutative polynomial rings on one and two indeterminates.
Smooth geometry of bi-quadratic algebras on three generators with PBW basis
Andrés Rubiano, Armando Reyes
In this paper, we investigate the differential smoothness of bi-quadratic algebras on three generators with PBW basis.