Search results for " Algebra"

Varieties of algebras with pseudoinvolution and polynomial growth

2017

Let A be an associative algebra with pseudoinvolution (Formula presented.) over an algebraically closed field of characteristic zero and let (Formula presented.) be its sequence of (Formula presented.) -codimensions. We shall prove that such a sequence is polynomially bounded if and only if the variety generated by A does not contain five explicitly described algebras with pseudoinvolution. As a consequence, we shall classify the varieties of algebras with pseudoinvolution of almost polynomial growth, i.e. varieties of exponential growth such that any proper subvariety has polynomial growth and, along the way, we shall give also the classification of their subvarieties. Finally, we shall de…

Lie Algebras Generated by Extremal Elements

1999

We study Lie algebras generated by extremal elements (i.e., elements spanning inner ideals of L) over a field of characteristic distinct from 2. We prove that any Lie algebra generated by a finite number of extremal elements is finite dimensional. The minimal number of extremal generators for the Lie algebras of type An, Bn (n>2), Cn (n>1), Dn (n>3), En (n=6,7,8), F4 and G2 are shown to be n+1, n+1, 2n, n, 5, 5, and 4 in the respective cases. These results are related to group theoretic ones for the corresponding Chevalley groups.

Introduction to Gestural Similarity in Music. An Application of Category Theory to the Orchestra

2019

Mathematics, and more generally computational sciences, intervene in several aspects of music. Mathematics describes the acoustics of the sounds giving formal tools to physics, and the matter of music itself in terms of compositional structures and strategies. Mathematics can also be applied to the entire making of music, from the score to the performance, connecting compositional structures to acoustical reality of sounds. Moreover, the precise concept of gesture has a decisive role in understanding musical performance. In this paper, we apply some concepts of category theory to compare gestures of orchestral musicians, and to investigate the relationship between orchestra and conductor, a…

Computing the Original eBWT Faster, Simpler, and with Less Memory

2021

Mantaci et al. [TCS 2007] defined the \(\mathrm {eBWT}\) to extend the definition of the \(\mathrm {BWT}\) to a collection of strings. However, since this introduction, it has been used more generally to describe any \(\mathrm {BWT}\) of a collection of strings, and the fundamental property of the original definition (i.e., the independence from the input order) is frequently disregarded. In this paper, we propose a simple linear-time algorithm for the construction of the original \(\mathrm {eBWT}\), which does not require the preprocessing of Bannai et al. [CPM 2021]. As a byproduct, we obtain the first linear-time algorithm for computing the \(\mathrm {BWT}\) of a single string that uses …

Quantization of Poisson Lie Groups and Applications

1996

LetG be a connected Poisson-Lie group. We discuss aspects of the question of Drinfel'd:can G be quantized? and give some answers. WhenG is semisimple (a case where the answer isyes), we introduce quantizable Poisson subalgebras ofC ∞(G), related to harmonic analysis onG; they are a generalization of F.R.T. models of quantum groups, and provide new examples of quantized Poisson algebras.

Estudios sobre el establecimiento de analogías en la resolución de problemas. Analogías en resolución de problemas de ciencias: efectos del contexto,…

2014

El trabajo de investigación que se presenta se enmarca en el programa de doctorado en Didácticas Específicas de la Universitat de València, dentro del itinerario de Investigación en Didáctica de las Ciencias Experimentales. El objetivo general de la presente investigación es la transferencia analógica en resolución de problemas y los factores que afectan a ésta. Analizamos la transferencia entre problemas verbales (en esta tesis ello significa lo mismo que problemas con enunciado escrito) de estructura algebraica porque constituyen una tipología de problemas de amplísima presencia en los currículos de enseñanza secundaria, tanto de ciencias como de matemáticas. Dentro de los procesos implic…

On the arithmetic and geometry of binary Hamiltonian forms

2011

Given an indefinite binary quaternionic Hermitian form $f$ with coefficients in a maximal order of a definite quaternion algebra over $\mathbb Q$, we give a precise asymptotic equivalent to the number of nonequivalent representations, satisfying some congruence properties, of the rational integers with absolute value at most $s$ by $f$, as $s$ tends to $+\infty$. We compute the volumes of hyperbolic 5-manifolds constructed by quaternions using Eisenstein series. In the Appendix, V. Emery computes these volumes using Prasad's general formula. We use hyperbolic geometry in dimension 5 to describe the reduction theory of both definite and indefinite binary quaternionic Hermitian forms.

An Arakelov inequality in characteristic p and upper bound of p-rank zero locus

2008

In this paper we show an Arakelov inequality for semi-stable families of algebraic curves of genus $g\geq 1$ over characteristic $p$ with nontrivial Kodaira-Spencer maps. We apply this inequality to obtain an upper bound of the number of algebraic curves of $p-$rank zero in a semi-stable family over characteristic $p$ with nontrivial Kodaira-Spencer map in terms of the genus of a general closed fiber, the genus of the base curve and the number of singular fibres. An extension of the above results to smooth families of Abelian varieties over $k$ with $W_2$-lifting assumption is also included.

Smooth structures on algebraic surfaces with cyclic fundamental group

1988

Automorphisms of hyperelliptic GAG-codes

2009

Abstract We determine the n –automorphism group of generalized algebraic-geometry codes associated with rational, elliptic and hyperelliptic function fields. Such group is, up to isomorphism, a subgroup of the automorphism group of the underlying function field.