Artículos (Álgebra)

URI permanente para esta colecciónhttps://hdl.handle.net/11441/10804

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Mostrando 1 - 20 de 314

On the behavior of modules of m-integrable derivations in the sense of Hasse-Schmidt under base change
(Elsevier, 2020-08-26) Tirado Hernández, María de la Paz; Álgebra; Instituto Universitario de Investigación de Matemáticas “Antonio de Castro Brzezicki” (IMUS)
We study the behavior of modules of m-integrable derivations of a commutative finitely generated algebra in the sense of Hasse-Schmidt under base change. We focus on the case of separable ring extensions over a field of positive characteristic and on the case where the extension is a polynomial ring in an arbitrary number of variables.
Leaps of modules of integrable derivations in the sense of Hasse-Schmidt
(Elsevier, 2020-04) Tirado Hernández, María de la Paz; Álgebra; Instituto Universitario de Investigación de Matemáticas “Antonio de Castro Brzezicki” (IMUS)
Let k be a commutative ring of characteristic p > 0. We prove that leaps of chain formed by modules of integrable derivations in the sense of Hasse-Schmidt of a k-algebra only occur at powers of p.
"Corrigendum to On the modules of m-integrable derivations in non-zero characteristic" [Adv. Math. 229 (2012) 2712–2740]
(Elsevier, 2024-06-07) Narváez Macarro, Luis; Álgebra; FQM218: Singularidades, Geometría Algebraica Aritmética, Grupos y Homotopía
Proposition (2.2.1) in “On the modules of m-integrable derivations in non-zero characteristic” is false for general finitely generated ideals I of our ambient polynomial or power series ring, but it was always used in the original article for principal ideals. Here we prove it under this hypothesis.
A computation of vanishing cycles with respect to irreductible plane-curves - applications to perverse sheaves
(L'Academie des Sciences, 1985) Narváez Macarro, Luis; Álgebra; FQM218: Singularidades, Geometría Algebraica Aritmética, Grupos y Homotopía
We describe the diagram of vector spaces representing the perverse complex of vanishing cycles, associated to a local system on the complement of an irreductible plane curve, in terms of the associated representation of the local fundamental group. This description give us a method to calculate the characetristic cycle of the intersection complexes, and also a combinatorial construction of perverse sheaves.
On the detection of knotted spheres by their traces in high dimensions
(arXiv, 2025-11-10) Bais, Valentina; Prisa, Alessio di; Hartman, Daniel; Hsueh, Chun-Sheng; Kegel, Marc; Merz, Alice; Pencovitch, Mark; Ray, Arunima; Santoro, Diego; Truöl, Paula; Wakelin, Laura; Álgebra
For every , we demonstrate the existence of non-isotopic smooth -knots in with diffeomorphic traces by generalising the RBG link construction to all dimensions. Conversely, we prove that for every , the unknot in is detected by the diffeomorphism type of its surgery and hence by its trace.
Links have no characterising slopes
(arXiv, 2025-11-26) Kegel, Marc; Schmalian, Misha; Álgebra
We show that there is no analogue of characterising slopes for multi-component links. Concretely, we show that for any ordered link L in S3 with n>1 components and any rational slopes r_1, ..., r_n, there are infinitely many links L_i with non-homeomorphic complements such that the Dehn fillings L(r_1, ..., r_n) and L_i(r_1, ..., r_n) are homeomorphic.
Braid positive surgery descriptions
(arXiv, 2025-12-16) Kegel, Marc; Truöl, Paula; Álgebra
In this short note, we prove that every closed, oriented, connected 3-manifold arises as Dehn surgery along a braid positive link.
Contact surgery distance
(arXiv, 2025-12-16) Kegel, Marc; Nonino, Isacco; Yadav, Monika; Álgebra
Inthisarticle, wedefinethecontactsurgerydistance of two contact 3-manifolds (𝑀,𝜉) and (𝑀′,𝜉′) as the minimal number of contact surgeries needed to obtain (𝑀,𝜉) from (𝑀′,𝜉′). Our main result states that the contact surgery distance between two contact 3-manifolds is at most 5 larger than the topological surgery distance between the underlying smooth manifolds. As a byproduct of our proof, we classify the rational homology 3-spheres on which the 𝑑3-invariant of a 2-plane field already determines its Γinvariant and Euler class.
Quantum algorithms for the sylvester denumerant and the numerical semigroup membership problem
(ArXiv, 2021) Ossorio Castillo, Joaquín; Tornero Sánchez, José María; Álgebra; FQM218: Singularidades, Geometría Algebraica Aritmética, Grupos y Homotopía
Two quantum algorithms are presented, which tackle well--known problems in the context of numerical semigroups: the numerical semigroup membership problem (NSMP) and the Sylvester denumerant problem (SDP).
A Geometric Approach to the Frobenius Unicity Conjecture for the Markoff Equation
(EMS, 2008) Tornero Sánchez, José María; Álgebra; FQM218: Singularidades, Geometría Algebraica Aritmética, Grupos y Homotopía
The long-standing Frobenius conjecture on the unicity of ordered solutions for the Markoff equation is translated in a very simple way into an arithmetic statement on the existence of integral points on certain hyperbolas. Some previous work of Kang and Melville can then be used for relating the problem to a statement concerning rank 2 symmetric hyperbolic Kac-Moody algebras.
On the computation of the MED closure of a numerical semigroup
(Springer, 2025-07-07) Jiménez Urroz, Jorge; Tornero Sánchez, José María; Álgebra; FQM218: Singularidades, Geometría Algebraica Aritmética, Grupos y Homotopía
Maximally embedding dimension (MED) numerical semigroups are a wide and interesting family, with some remarkable algebraic and combinatorial properties. It is well-known that one can construct an MED closure associated to any numerical semigroup. This paper shows two different explicit methods to construct this closure which also shed new light on the very nature of this object.
Enheduanna, Teano y Aglaonike, precursoras de Hipatia
(Sociedad Puig Adam de Profesores de Matemáticas, 2010-06) Núñez Valdés, Juan; Olivares Nadal, Alba Victoria; Rodríguez, Estrella; Silvero Casanova, Marithania; Álgebra; FQM218: Singularidades, Geometría Algebraica Aritmética, Grupos y Homotopía
Most researchers on the History of Science, as well as historians trying to popularize Mathematics among wide audiences tend to believe that Hipatia of Alexandria (century IV B.C.) is the first woman to have been a fist-rate mathematician in the ancient world. However, the authors of this paper remind the figure of three women living in earlier times than those of Hipatia, who could well deserve an analogous consideration as forerunners of female mathematics, namely Enheduanna (century XXV B.C.), Theano of Croto (century VI B.C.) and Aglaonike (century III B.C.)
Quantum Annular Homology and Bigger Burnside Categories
(Springer, 2024-07-01) Cantero Morán, Federico; García Rodrigo, Sergio; Silvero Casanova, Marithania; Álgebra; FQM218: Singularidades, Geometría Algebraica Aritmética, Grupos y Homotopía
As part of their construction of the Khovanov spectrum, Lawson, Lipshitz and Sarkar assigned to each cube in the Burnside category of finite sets and finite correspondences, a finite cellular spectrum. In this paper, we extend this assignment to cubes in Burnside categories of infinite sets. This is later applied to the work of Akhmechet, Krushkal and Willis on the quantum annular Khovanov spectrum with an action of a finite cyclic group: we obtain a quantum annular Khovanov spectrum with an action of the infinite cyclic group.
Khovanov homology, wedges of spheres and complexity
(Springer, 2024-05-02) Przytycki, Jozef H.; Silvero Casanova, Marithania; Álgebra; FQM218: Singularidades, Geometría Algebraica Aritmética, Grupos y Homotopía
Our main result has topological, combinatorial and computational flavor. It is motivated by a fundamental conjecture stating that computing Khovanov homology of a closed braid of fixed number of strands has polynomial time complexity. We show that the independence simplicial complex I(w) associated to the 4-braid diagram w (and therefore its Khovanov spectrum at extreme quantum degree) is contractible or homotopy equivalent to either a sphere, or a wedge of two spheres (possibly of different dimensions), or a wedge of three spheres (at least two of them of the same dimension), or a wedge of four spheres (at least three of them of the same dimension). On the algorithmic side we prove that finding the homotopy type of I(w) can be done in polynomial time with respect to the number of crossings in w. In particular, we prove the wedge of spheres conjecture for circle graphs obtained from 4-braid diagrams. We also introduce the concept of Khovanov adequate diagram and discuss criteria for a link to have a Khovanov adequate braid diagram with at most 4 strands.
On Euler-Homogeneity for free divisors
(ArXiv, 2023-09-16) Valle Rodríguez, Abraham del; Álgebra
In 2002, it was conjectured that a free divisor satisfying the so-called Logarithmic Comparison Theorem must be strongly Euler-homogeneous and it was proved for the two-dimensional case. Later, in 2006, it was shown that the conjecture is also true in dimension three, but, today, the answer for the general case remains unknown. In this paper, we use the decomposition of a singular derivation as the sum of a semisimple and a topologically nilpotent derivation that commute in order to deal with this problem. By showing that this decomposition preserves the property of being logarithmic, we are able to give alternative proofs for the low-dimensional known cases.
Reduced Kronecker Coefficients
(Universidad de Granada, 2008) Briand, Emmanuel; Orellana, Rosa C.; Rosas Celis, Mercedes Helena; Álgebra; FQM333: Algebra Computacional en Anillos no Conmutativos y Aplicaciones
Rigid local systems with monodromy group the Conway group Co3
(Elsevier, 2019-09-27) Katz, Nicholas M.; Rojas León, Antonio; Tiep, Pham Huu; Álgebra; FQM218: Singularidades, Geometría Algebraica Aritmética, Grupos y Homotopía
We first develop some basic facts about certain sorts of rigid local systems on the affine line in characteristic p>0. We then apply them to exhibit a number of rigid local systems of rank 23 on the affine line in characteristic p=3 whose arithmetic and geometric monodromy groups are the Conway group Co3 in its orthogonal irreducible representation of degree 23.
Sumas exponenciales: otra forma de contar
(Real Academia Sevillana de Ciencias, 2009-11-30) Rojas León, Antonio; Álgebra; FQM218: Singularidades, Geometría Algebraica Aritmética, Grupos y Homotopía
Las sumas exponenciales (o sumas trigonométricas) han jugado un papel importante en el desarrollo de la teoría de números desde tiempos de Gauss, cuando fueron utilizadas para probar la ley de reciprocidad cuadrática. Con el desarrollo de las teorías de cohomologías de Weil durante la segunda mitad del siglo pasado se dio un nuevo impulso a su estudio usando métodos geométricos. En su definición más general, una suma exponencial es simplemente una suma de raíces de la unidad en C. En este artículo nos centraremos en sumas de caracteres aditivos o multiplicativos, aplicados a los valores de un cierto polinomio o función regular de nida sobre una variedad algebraica con coeficientes en un cuerpo finito. Repasaremos sus principales propiedades y los resultados más importantes de acotación conocidos.
Exposición de méritos de investigación, por el Dr. D. Antonio Rojas León, Premio "Real Maestranza de Caballería de Sevilla"
(Real Academia Matemática de Ciencias, 2009) Rojas León, Antonio; Álgebra; FQM218: Singularidades, Geometría Algebraica Aritmética, Grupos y Homotopía
On some Airy sheaves of Laurent type
(Springer, 2024-11-06) Katz, Nicholas M.; Rojas León, Antonio; Tiep, Pham Huu; Álgebra; FQM218: Singularidades, Geometría Algebraica Aritmética, Grupos y Homotopía
We study certain one-parameter families of exponential sums of Airy–Laurent type. Their general theory was developed in Katz and Tiep (Airy sheaves of Laurent type: an introduction, https://web.math.princeton.edu/~nmk/kt31_11sept.pdf). In the present paper, we make use of that general theory to compute monodromy groups in some particularly simple families (in the sense of “simple to remember"), realizing Weyl groups of type E6 and E8.

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