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math.DG2026
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…
math.DG2026
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…
math.DG2025
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…