Related papers: Methods of algebraic manipulation in perturbation …
In this note, we observe a relation between dialgebras (in particular, Leibniz algebras) and conformal algebras. The purpose is to show how the methods of conformal algebras help solving problems on dialgebras, and, conversely, how the…
The theory of operads (May, cyclic, modular, PROPs, etc) is extended to include higher dimensional phenomena, i.e. operations between operations, mimicking the algebraic structure on varieties of arbitrary dimensions, having marked…
We discuss some basic problems and conjectures in a program to construct general orbifold conformal field theories using the representation theory of vertex operator algebras. We first review a program to construct conformal field theories.…
The chapter provides an introduction to the basic concepts of Algebraic Topology with an emphasis on motivation from applications in the physical sciences. It finishes with a brief review of computational work in algebraic topology,…
Our Chapter in the upcoming Volume I: Computer Science and Software Engineering of Computing Handbook (Third edition), Allen Tucker, Teo Gonzales and Jorge L. Diaz-Herrera, editors, covers Algebraic Algorithms, both symbolic and numerical,…
We demonstrate the use of several tools from Algebraic Combinatorics such as Young tableaux, symmetry operators, the Littlewood-Richardson rule and discrete Fourier transforms of symmetric groups in investigations of algebraic curvature…
This paper is a short introduction to orthogonal polynomials, both the general theory and some special classes. It ends with some remarks about the usage of computer algebra for this theory.
This survey gives an overview of several fundamental algebraic constructions which arise in the study of splines. Splines play a key role in approximation theory, geometric modeling, and numerical analysis, their properties depend on…
An introduction to the applications of algebraic surgery to the structure theory of high-dimensional topological manifolds.
In this paper we define a class of polynomial functors suited for constructing coalgebras representing processes in which uncertainty plays an important role. In these polynomial functors we include upper and lower probability measures,…
This is a short exposition--mostly by way of the toy models ``double logarithm'' and ``triple logarithm''--which should serve as an introduction to a forthcoming article in which we establish a connection between multiple polylogarithms,…
We propose an approach to image processing related to algebraic operators acting in the space of images. In view of the interest in the applications in optics and computer science, mathematical aspects of the paper have been simplified as…
These lecture notes, suitable for a two-semester introductory course or self-study, offer an elementary and self-contained exposition of the basic tools and concepts that are encountered in practical computations in perturbative thermal…
The tridiagonal representation approach is an algebraic method for solving second order differential wave equations. Using this approach in the solution of quantum mechanical problems, we encounter two new classes of orthogonal polynomials…
Moving from the mathematical theory of (abstract) syntax, we develop a general relational theory of symbolic manipulation parametric with respect to, and accounting for, general notions of syntax. We model syntax relying on categorical…
The interplay rich between algebraic geometry and string and gauge theories has recently been immensely aided by advances in computational algebra. However, these symbolic (Gr\"{o}bner) methods are severely limited by algorithmic issues…
Some introductory concepts and basic definitions of the Lie superalgebras and their quantum deformations are exposed. Especially the induced representation methods in both cases are described. Based on the Kac representation theory we have…
A long-term research proposal on the algebraic structure, the representations and the possible applications of paraparticle algebras is structured in three modules: The first part stems from an attempt to classify the inequivalent gradings…
The relation between algebraic and traditional calculations of molecular vibrations is investigated. An explicit connection between interactions in configuration space and the corresponding algebraic interactions is established.
We discuss the use of methods coming from integrable systems to study problems of enumerative and algebraic combinatorics, and develop two examples: the enumeration of Alternating Sign Matrices and related combinatorial objects, and the…