Artículos (Álgebra)

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

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Mostrando 1 - 20 de 306

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.
Presentación de los Premiados por el Ilmo. Sr. D. Luis Narváez Macarro, Académico Nunzerario
(Real Academia Sevillana de Ciencias, 2002-06-06) Narváez Macarro, Luis; Álgebra; FQM218: Singularidades, Geometría Algebraica Aritmética, Grupos y Homotopía
Hasse–Schmidt modules versus integrable connections
(Springer, 2019-12-16) Narváez Macarro, Luis; Álgebra; FQM218: Singularidades, Geometría Algebraica Aritmética, Grupos y Homotopía
We prove that, in characteristic 0, any Hasse–Schmidt module structure can be recovered from its underlying integrable connection, and consequently Hasse–Schmidt modules and modules endowed with an integrable connection coincide.
Conclusiones y propuestas surgidas a partir de la Reunión de Directores de Institutos Universitarios de Matemáticas celebrada en la UCM el 25 de febrero de 2010
(Real Sociedad Matemática Española, 2010-02-25) Bonet Solves, José Antonio; Herrero, Miguel Ángel; Narváez Macarro, Luis; Álgebra; FQM218: Singularidades, Geometría Algebraica Aritmética, Grupos y Homotopía
El pasado 25 de febrero de 2010 se celebró en la Universidad Complutense de Madrid una reunión de Directores (o representantes) de Institutos Universitarios de Investigación de Matemáticas con el objeto de estudiar posibles colaboraciones y de establecer unas bases para ello. A dicha reunión asistieron: Isabel Bermejo Díaz (CIMAC, Canarias), José Bonet Solves (IUMPA, Universidad Politécnica de Valencia), Fernando Casas Pérez (IMAC, Universidad de Castellón), Miguel Á. Herrero García (IMI, Universidad Complutense de Madrid), Henar Herrero Sanz (IMACI, Universidad de Castilla-La Mancha), Lucas Jódar Sánchez (IUMM, Universidad Politécnica de Valencia), Àngel Jorba Monte (IMUB, Universidad de Barcelona), Juan I. Montijano Torcal y Luis Rández García (IUMA, Universidad de Zaragoza), Luis Narváez Macarro (IMUS, Universidad de Sevilla), Juan J. Nieto Roig (Instituto de Matemáticas, Universidad de Santiago). En la preparación de dicha reunión también participó Tomás Tejero Prieto (IUFFM, Universidad de Salamanca). A continuación se resumen los temas tratados en dicha reunión. Muchos de los comentarios que siguen son aplicables a cualquier tipo de Instituto Universitario de Investigación (IUI), aunque por simplicidad nos referiremos solamente a los Institutos Universitarios de Matemáticas (IUM).
Finiteness of leaps in the sense of Hasse-Schmidt of unibranch curves in positive characteristic
(Elsevier, 2023-12-06) Narváez Macarro, Luis; Reguera, Ana J.; Tirado Hernández, María de la Paz; Álgebra; FQM218: Singularidades, Geometría Algebraica Aritmética, Grupos y Homotopía
We prove that the set of leaps of the chain of m-integrable derivations of a curve X over a perfect field with geometrically unibranch singularities is finite. This result is a consequence of an affirmative answer to Seidenberg's question of extending, in positive characteristic, Hasse–Schmidt derivations of finite length of the local rings of X to their integral closures.
The proper L-S category of Whitehead manifolds
(Elsevier, 2005-03-03) Cárdenas Escudero, Manuel Enrique; Muro Jiménez, Fernando; Quintero Toscano, Antonio Rafael; Álgebra; FQM218: Singularidades, Geometría Algebraica Aritmética, Grupos y Homotopía
It is shown that the proper L-S category of an eventually end-irreducible, -irreducible Whitehead 3-manifold is 4. For this we prove, in the category of germs at infinity of proper maps, a partial analogue of the characterization by Eilenberg and Ganea of the L-S category of an aspherical space.
The homotopy category of pseudofunctors and translation cohomology
(Elsevier, 2007-05-05) Baues, Hans Joachim; Muro Jiménez, Fernando; Álgebra; FQM218: Singularidades, Geometría Algebraica Aritmética, Grupos y Homotopía
We develop the obstruction theory of the 2-category of abelian track categories, pseudofunctors and pseudonatural transformations by using the cohomology of categories. The obstructions are defined in Baues–Wirsching cohomology groups. We introduce translation cohomology to classify endomorphisms in the 2-category of abelian track categories. In a sequel to this paper we will show, under certain conditions which are satisfied by all homotopy categories, that a translation cohomology class determines the exact triangles of a triangulated category.
Proper L-S category, fundamental pro-groups and 2-dimensional proper co-H-spaces
(Elsevier, 2005-03-08) Cárdenas Escudero, Manuel Enrique; Fernández Lasheras, Francisco Jesús; Muro Jiménez, Fernando; Quintero Toscano, Antonio Rafael; Álgebra; FQM218: Singularidades, Geometría Algebraica Aritmética, Grupos y Homotopía
This paper presents a study of one-ended locally finite CW-complexes with proper L–S category ⩽2. We detect the class of towers of groups which can be the fundamental pro-group of a space of proper L–S category 2. A second part of the paper is concerned with two-dimensional CW-complexes. For these, we give different characterizations of spaces with proper L–S category ⩽2.
Exposición de méritos de investigación, por el Dr. D. Fernando Muro Jiménez, Premio "Real Academia Sevillana de Ciencias"
(Real Academia Sevillana de Ciencias, 2011) Muro Jiménez, Fernando; Álgebra; FQM218: Singularidades, Geometría Algebraica Aritmética, Grupos y Homotopía

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