相关论文: Foundations of algebraic surgery

An introduction to the applications of algebraic surgery to the structure theory of high-dimensional topological manifolds.

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,…

This paper is an introduction to the use of the cobordism of chain complexes with Poincar\'e duality in surgery theory. It is a companion to the author's paper "An introduction to algebraic surgery" math.AT/0008071 (to appear in Volume 2 of…

In this paper we introduce elements of algebraic geometry over an arbitrary algebraic structure. We prove Unification Theorems which gather the description of coordinate algebras by several ways.

We review definitions and basic properties of operads, PROPs and algebras over these structures.

A very elementary introduction to quantum algebras is presented and a few examples of their physical applications are mentioned.

We give a general account of family algebras over a finitely presented linear operad, this operad together with its presentation naturally defining an algebraic structure on the set of parameters.

We give an elementary introduction to the theory of supermembranes.

This paper is a survey of computational issues in algebraic geometry, with particular attention to the theory of Grobner bases and the regularity of an algebraic variety. 1. A geometric introduction to Grobner bases. 2. An algebraic…

Lectures notes in universal algebraic geometry for beginners

Algebraic basics on Temperley-Lieb algebras are proved in an elementary and straightforward way with the help of tensor categories behind them.

Some examples and basic properties of ultrametric spaces are briefly discussed.

An algebraic technique adapted to the problems of the fundamental theoretical physics is presented. The exposition is an elaboration and an extension of the methods proposed in previous works by the aut

The purpose of this note is to provide a gentle introduction to basic universal algebra and (abstract) clones.

After an historical introduction on the standard algebraic approach to quantum mechanics of large systems we review the basic mathematical aspects of the algebras of unbounded operators. After that we discuss in some details their relevance…

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…

We give an introduction to the theory of initial ideals and initial algebras with emphasis on the transfer of structural properties.

This paper examines the concept of gluing, placing it within its most general categorical context and tracing its foundational role in the broader architecture of algebraic geometry.

We give a conceptual explanation of universal deformation formulas for unital associative algebras and prove some results on the structure of their moduli spaces. We then generalize universal deformation formulas to other types of algebras…

An algebraic deformation theory of coalgebra morphisms is constructed.