Alejandro Piñera Nicolás

University of Oviedo | UNIOVI · Department of Mathematics

We study irreducible characters, and define and study supercharacters of the adjoint group of a finite radical ring. We extend work of Halasi on irreducible characters, and recent work of Diaconis and Isaacs on supercharacters of algebra groups defined over finite fields, and derive some consequences for the representation theory of compact p-adic...

The structure of additive multivariable codes over ${\mathbb{F}_4}$ (the Galois field with 4 elements) is presented. The semisimple case (i.e., when the defining polynomials of the code have no repeated roots) is specifically addressed. These codes extend in a natural way the abelian codes, of which additive cyclic codes of odd length are a parti...

Some identities satisfied by certain standard composition algebras, of types II and III, are studied and become candidates for the characterization of the mentioned types. Composition algebras of arbitrary dimension, over a field F with char(F)≠2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackag...

In this work we present a standard model for Galois rings based on the standard model of their residual fields, that is, a a sequence of Galois rings starting with Zpr\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setl...

In this work, we present a standard model for Galois rings based on the standard model of their residual fields, that is, a sequence of Galois rings starting with ${\mathbb Z}_{p^r} that coves all the Galois rings with that characteristic ring and such that there is an algorithm producing each member of the sequence whose input is the size of the r...

Inspired by circular complex interval arithmetic, an arithmetic for closed balls in ℝⁿ is pursued. In this sense, the properties of certain operations on closed balls in ℝⁿ, some of which related either to the Hadamard product of vectors or to the 2-fold vector cross product when n ∈ {3,7}, are studied. In particular, known results for operations o...

Nonassociative algebra plays a fundamental role in the description of physical systems. Symmetry is related to the transformations of these algebras, which are controlled by their automorphisms group. Starting from the known structure of finite division rings with 64 elements, we construct some nonassociative finite division algebra of Orders 256 a...

Through a matrix approach of the $2$-fold vector cross product in $\mathbb{R}^3$ and in $\mathbb{R}^7$, some vector cross product differential and difference equations are studied. Either the classical theory or convenient Drazin inverses, of elements belonging to the class of index $1$ matrices, are applied.

We consider codes defined over an affine algebra $\mathcal A=R[X_1,\dots,X_r]/\left\langle t_1(X_1),\dots,t_r(X_r)\right\rangle$, where $t_i(X_i)$ is a monic univariate polynomial over a finite commutative chain ring $R$. Namely, we study the $\mathcal A-$submodules of $\mathcal A^l$ ($l\in \mathbb{N}$). These codes generalize both the codes over f...

A study of real skew-symmetric matrices of orders 7 and 8, defined through the vector cross product in R^7, is presented. More concretely, results on matrix properties, eigenvalues, (generalized) inverses and rotation matrices are established.

In this work, we study the structure of multivariable modular codes over finite chain rings when the ambient space is a principal ideal ring. We also provide some applications to additive modular codes over the finite field .

Global and local positioning systems (LPS) make use of nonlinear equations systems to calculate coordinates of unknown points. There exist several methods, such as Sturmfels’ resultant, Groebner bases and least squares, for dealing with this kind of equations. We introduce two methods for solving this problem with the aid of symbolic techniques rel...

Mais vezes do que o desejável ocorre um erro: (x + y)2 = x2 + y2. Mas será sempre um erro? Veremos que não! Mas, no rigor da Matemática, há que saber o contexto em que se trabalha... Nomeadamente na Álgebra Tropical, área com aplicações na Criptografia, é uma identidade!

We study the associative triple system of the second kind 𝒜 obtained from a new multiplication defined in the underlying vector space of the four-dimensional ternary Filippov algebra A4. Descriptions of the automorphisms group and the antiautomorphisms set of 𝒜, both constituted by certain orthogonal matrices, are presented. Through a Leibniz-type...

In this work, we study the structure of multivariable modular codes over finite chain rings when the ambient space is a principal ideal ring. We also provide some applications to additive modular codes over the finite field F4.

Additive multivariate codes over F4F4 (the Galois field with 4 elements) are a natural extension of additive cyclic and abelian codes. A complete description of such codes when the length is odd was presented in [11]. In this paper we study some properties of this family of codes in the case when the length is even (modular case) and the number of...

Codes over finite commutative chain rings have been introduced as a generalization of codes over finite fields. Let S|RS|R be a Galois extension of finite commutative chain rings. If C⊆SnC⊆Sn is an S-code, it is possible to define, starting from C, two different R-codes: Res(C)=C∩RnRes(C)=C∩Rn and Tr(C)Tr(C), where Tr is the trace function. In this...

We use the theory of resultants of polynomials to study the stability of an arbitrary polynomial over a finite field, that is, the property of having all its iterates irreducible. This result partially generalises the quadratic polynomial case described by R. Jones and N. Boston. Moreover, for characteristic three, we show that certain polynomials...

In this text we study the exp − log functors for the categories of uniform groups and uniform Lie algebras.

This article studies a simple 4-dimensional ternary algebra 𝒜 which appears analogously to the quaternions from the Lie algebra 𝔰𝔩(2). We describe the heights 1 and 2 identities, and the derivations of 𝒜. Based on 𝒜, some ternary enveloping algebras for ternary Filippov algebras are constructed.

In this article we study relations between groups and quantum error correcting codes. Groups of central type are used to construct quantum error correcting codes. Both stabilizer and Clifford codes can be derived from a construction involving this kind of groups. A more general construction of Clifford codes will be given and their correcting prope...

ChemInform is a weekly Abstracting Service, delivering concise information at a glance that was extracted from about 100 leading journals. To access a ChemInform Abstract of an article which was published elsewhere, please select a “Full Text” option. The original article is trackable via the “References” option.

In this work we obtain a nontrivial estimate for the size of the set of triples (a,b,c)∈Fq∗×Fq×Fq which correspond to stable quadratic polynomials f(X)=aX2+bX+c over the finite field Fq with q odd. This estimate is an improvement of the bound O(q11/4) conjectured in a recent work of A. Ostafe and I. Shparlinski.

Let p be a prime, G a finite p-group, r the rank of G and e the exponent of G. In this short note we will prove that the exponent of the Schur multiplier of G divides pe+r⌈log2(rlog2p+1p−1)⌉.

ChemInform is a weekly Abstracting Service, delivering concise information at a glance that was extracted from about 100 leading journals. To access a ChemInform Abstract of an article which was published elsewhere, please select a “Full Text” option. The original article is trackable via the “References” option.

ChemInform is a weekly Abstracting Service, delivering concise information at a glance that was extracted from about 100 leading journals. To access a ChemInform Abstract of an article which was published elsewhere, please select a “Full Text” option. The original article is trackable via the “References” option.

ChemInform is a weekly Abstracting Service, delivering concise information at a glance that was extracted from about 100 leading journals. To access a ChemInform Abstract of an article which was published elsewhere, please select a “Full Text” option. The original article is trackable via the “References” option.

We review different group based algorithms for matrix multiplication and discuss the relations between the combinatorial properties of the used group and the complexity of these algorithms. We introduce a variant of an algorithm based on the ideas exposed in [H. Cohn, R. Kleinberg and B. Szegedy, in: FOCS 2005: 46th Annual IEEE Symposium on Foundat...

En esta tesis se estudia la extensión del concepto de Super-carácter, introducido originariamente para grupos de matrices unitriangulares, a grupos de la forma G=1+J, con J el radical de Jacobson de un álgebra asociativa de dimensión finita. Este concepto se extiende también al caso en el que el álgebra se sustituye por un R-módulo libre con R un a...

Algebraic methods play an important role in coding theory. For instance, there are many connections between codes and groups. In this paper we present two results that show different applications of algebraic methods in coding theory. One of them refers to the classical context and another one to the quantum error correcting theory. These results c...

Preparation of enantiomerically pure α‘-amino α,β-epoxy ketones 2 in an efficient synthesis starting from α‘-amino bromomethyl ketones 5 and the obtention of amino diepoxido 10a as synthetic application of 2 are described. We also report the generalization of the synthesis of 1-aminoalkyl halomethyl ketones to their bromo derivatives.

New reactions of alkynylcarbene complexes with 2-amino-1,3-dienes are reported. The reactions involve a first [4+2] cycloaddition step followed by a cyclopentannulation process that generates a molecule containing a cyclopentadiene moiety capable of undergoing a new [4+2] cycloaddition reaction with the carbene complex. The process can be controlle...