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Loop Groups (Oxford Mathematical Monographs)

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Loop Groups (Oxford Mathematical Monographs) Cover

 

Synopses & Reviews

Publisher Comments:

Loop groups, the simplest class of infinite dimensional Lie groups, have recently been the subject of intense study. This book gives a complete and self-contained account of what is known about them from a geometrical and analytical point of view, drawing together the many branches of mathematics from which current theory developed--algebra, geometry, analysis, combinatorics, and the mathematics of quantum field theory. The authors discuss loop groups' applications to simple particle physics and explain how the mathematics used in connection with loop groups is itself interesting and valuable, thereby making this work accessible to mathematicians in many fields.

Synopsis:

This book gives a complete and self-contained account of what is known about this subject and is written from a geometrical and analytical point of view, with quantum field theory very much in mind.

Description:

Includes bibliographical references (p. [304]-310).

Table of Contents

1. Introduction

PART I

2. Finite Dimensional Lie Groups

3. Groups of Smooth Maps

4. Central Extensions

5. The Root System: Kac-Moody Algebras

6. Loop Groups as Groups of Operators in Hilbert Space

7. The Grasmannian of Hilbert Space and the Determinant Time Bundle

8. The Fundamental Homogeneous Space

PART II

9. Representation Theory

10. The Fundamental Representation

11. The Borel-Weil Theory

12. The Spin Representation

13. 'Blips' or 'Vertex-Operators'

14. The Kac Character Formula and the Bernstein-Gelfand-Gelfand Resolution

Product Details

ISBN:
9780198535614
With:
Graeme, Segal
Author:
Segal, Graeme
Author:
Pressley, Andrew
Author:
null, Andrew
Author:
null, Graeme
Author:
Graeme, Segal
Publisher:
OUP Oxford
Location:
Oxford :
Subject:
Physics
Subject:
Mathematics
Subject:
Algebra - Linear
Subject:
Geometry, analytic
Subject:
Mathematics | Pure Mathematics
Subject:
Mathematics-Linear Algebra
Edition Description:
1st paperback with corrections
Series:
Oxford Mathematical Monographs
Series Volume:
no. 11
Publication Date:
19880631
Binding:
TRADE PAPER
Grade Level:
Professional and scholarly
Language:
English
Illustrations:
tables, boxes, graphs
Pages:
328
Dimensions:
9.24x6.14x.84 in. 1.13 lbs.

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Loop Groups (Oxford Mathematical Monographs) New Trade Paper
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Product details 328 pages Oxford University Press - English 9780198535614 Reviews:
"Synopsis" by , This book gives a complete and self-contained account of what is known about this subject and is written from a geometrical and analytical point of view, with quantum field theory very much in mind.
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