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Andrés Rubiano

Publications and source records attributed to Andrés Rubiano.

18 recordsLinked to original sources
arXiv2026

An Algebraic View of Amenable Groupoids

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 the unit space. The unanchored bisectional condition is exactly algebraic amenability of the Steinberg algebra, whereas the anchored version recovers ordinary amenability for one-unit groupoids and detects behavior invisible to the unanchored theory. We establish permanence under isomorphisms, open invariant reductions, disjoint unions, finite products, directed unions and AF approximations, while arbitrary subgroupoids need not inherit the property. For countable transitive discrete groupoids, infinite unit spaces are amenable through range escape, whereas finite unit spaces are amenable precisely when their isotropy groups are. This yields a characterization of hereditary algebraic amenability in terms of isotropy.

math.RA↗
arXiv2026

Normal Ordering and Stirling-Type Combinatorics for Double Ore Extensions of Type (14641)

We develop an explicit PBW normal ordering theory for the $26$ double extension regular algebras of type $(14641)$ in the Zhang-Zhang classification. With respect to the order $x_1\prec x_2\prec y_1\prec y_2$, we obtain closed two-letter formulas for the internal relations and recursive coefficient systems for mixed words, products of PBW monomials, powers of normal blocks, and noncommutative multinomial expressions. The internal coefficients are mostly quantum or skew-commutative, while the Jordan families produce Lah-Whitney, hence Stirling-type, triangular arrays. The symbolic reductions are supported by a SageMath implementation included as an ancillary file.

math.CO↗
arXiv2026

Combinatorial aspects of normal ordering of 3-dimensional skew polynomial rings

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 help of the Mathematical software \texttt{SageMath}, we are able to reduce the length of computation of PBW forms and normal orderings appearing in commutation rules of these algebras.

math.CO↗
arXiv2026

A note on explicit homological invariants of graded double Ore extensions

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 resolution and graded Betti numbers of the trivial right module and also compute linear resolutions for two natural cyclic right modules. This provides a concrete link between the PBW structure of the algebra and the homological behavior of its natural quotients.

math.RA↗
arXiv2026

On the smoothness of 3-dimensional skew polynomial rings

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 family 3-dimensional skew polynomial rings characterized by Bell and Smith \cite{BellSmith1990}.

math.DG↗
arXiv2026

On differential smoothness of certain Artin-Schelter regular algebras of dimension 5

This article investigates the differential smoothness of various five-dimensional Artin-Schelter regular algebras. By analyzing the relationship between the number of generators and the Gelfand-Kirillov dimension, we provide structural obstructions to differential smoothness in specific algebraic families. In particular, we prove that certain two- and four-generator AS-regular algebras of global dimension five fail to admit a differential calculus, while a five-generator graded Clifford algebra provides a contrasting positive example.

math.RA↗
arXiv2026

Center of double extension regular algebras of type (14641)

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 of the analysis is supported by computations in SageMath. As an application, we provide new examples related to the Zariski cancellation problem.

math.RA↗
arXiv2025

On the annihilator condition for skew PBW extensions

We investigate the annihilator condition $(a.c.)$ for skew Poincaré-Birkhoff-Witt extensions. We prove that some results about the annihilator condition $(a.c.)$ for skew polynomial rings also hold for skew PBW extensions. We also demonstrate that the behavior of annihilators is determined by the defining relations of the extension. Our results extend those corresponding presented for skew polynomial rings

math.RA↗
arXiv2025

A view toward the smooth geometry of Sklyanin algebras

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 of the four-dimensional Sklyanin algebras admit a connected integrable differential calculus of suitable dimension.

math.DG↗