相关论文: K-theory. An elementary introduction

These are notes from a 15 week course aimed at graduate mathematicians. They provide an essentially self-contained introduction to some of the ideas and terminology of QFT.

Following Hopkins and Singer, we give a definition for the differential equivariant K-theory of a smooth manifold acted upon by a finite group. The ring structure for differential equivariant K-theory is developed explicitly. We also…

In these notes, we present a rigorous and self-contained introduction to the fundamental concepts and methods of quantum many-body theory. The text is designed to provide a solid theoretical foundation for the study of interacting quantum…

Some topics which can be easily explained to undergraduate students are presented, with elementary derivations. For a more systematic treatment of heavy-quark physics, see the textbook by Manohar and Wise.

These notes are a self-contained introduction to Galois theory, designed for the student who has done a first course in abstract algebra.

This paper is a guide for the pure mathematician who would like to know more about cryptography based on group theory. The paper gives a brief overview of the subject, and provides pointers to good textbooks, key research papers and recent…

The article gives the second part of the treatise on Regular Algebraic $K$-theory (Sections V & VI) of the author. Regular algebraic $K$-theory for groups is a homology theory for discrete groups closely connected to (but different from)…

We investigate modules over "systematic" rings. Such rings are "almost graded" and have appeared under various names in the literature; they are special cases of the G-systems of Grzeszczuk. We analyse their K-theory in the presence of…

This paper is an elaboration of an introductory talk given by the author at a workshop on Clifford algebras at Tennessee Technical University, in May 2002. We give an introduction to the basic concepts of Clifford analysis, including links…

This book provides an introduction to the mathematical analysis of deep learning. It covers fundamental results in approximation theory, optimization theory, and statistical learning theory, which are the three main pillars of deep neural…

Some very elementary ideas about quantum groups and quantum algebras are introduced and a few examples of their physical applications are mentioned.

This is a survey on the topic explained in the title, for the proceedings on the K-theory 1997 summer institute in Seattle.

An introduction in quantum mechanical theory for NMR students which covers basic concepts and calculations.

We define E-theory for separable C*-algebras over second countable topological spaces and establish its basic properties. This includes an approximation theorem that relates the E-theory over a general space to the E-theories over finite…

We describe Universal Coefficient Theorems for the equivariant Kasparov theory for C*-algebras with an action of the group of integers or over a unique path space, using KK-valued invariants. We compare the resulting classification up to…

Let a compact group G act on real or complex C*-algebras A and B, with A separable and B sigma-unital. We express the G-equivariant Kasparov groups KK_n(A,B) by algebraic K-groups of a certain additive category.

Statistical learning theory provides the theoretical basis for many of today's machine learning algorithms. In this article we attempt to give a gentle, non-technical overview over the key ideas and insights of statistical learning theory.…

k-graphs are higher-rank analogues of directed graphs which were first developed to provide combinatorial models for operator algebras of Cuntz-Krieger type. Here we develop the theory of covering spaces for k-graphs, obtaining a…

We survey three different ways in which K-theory in all its forms enters quantum field theory. In Part 1 we give a general argument which relates topological field theory in codimension two with twisted K-theory, and we illustrate with some…

This is a short, self-contained expository survey, focused on algebraic and analytic aspects of quantum groups. Topics covered include the definition of ``quantum group,'' the Yang-Baxter equation, quantized universal enveloping algebras,…