2 edition of **Affine Lie Algebras and Quantum Groups** found in the catalog.

Affine Lie Algebras and Quantum Groups

JГјrgen A. Fuchs

- 344 Want to read
- 19 Currently reading

Published
**October 30, 1992**
by Cambridge University Press
.

Written in English

- Linear algebra,
- Theoretical methods,
- Lie algebras,
- Science / Mathematical Physics,
- Mathematical Physics,
- Lie Groups,
- Quantum field theory,
- Quantum groups,
- Science/Mathematics

The Physical Object | |
---|---|

Format | Hardcover |

Number of Pages | 447 |

ID Numbers | |

Open Library | OL7740025M |

ISBN 10 | 0521415934 |

ISBN 10 | 9780521415934 |

Using the theory of realization of affine algebras, construct an untwisted affine KM algebra A 3 (1) from that of A 3. (ii) Using the theory of realization of affine algebras, construct a twisted affine KM algebra D 3 (2) from that of D 3. Prove that in the usual notation, the root aα 1 + 2α 2 is a special imaginary root for G (A), where. The theory developed in the book includes the case of quantum affine enveloping algebras and, more generally, the quantum analogs of the Kac–Moody Lie algebras. Introduction to Quantum Groups will be of interest to mathematicians working in the representation theory of Lie groups and Lie algebras, knot theorists, theoretical physicists, and Brand: Birkhäuser Basel.

Quantum Lie algebras are generalizations of Lie algebras whose structure constants are power series in h. They are derived from the quantized envelop-ing algebras U h(g). The quantum Lie bracket satisﬁes a generalization of antisymmetry. Representations of quantum Lie algebras are deﬁned in terms of a generalized commutator. to an arbitrary Kac-Moody algebra, in particular, to the affine Lie algebra 0 associated to g. We will call, for shortness, Uq(g) quantum algebra, and Uq(O) quantum affine algebra. It was gradually realized that the WZNW conformal field theory and the represen- tation theory of quantum groups have a profound link.

The ﬁrst part is dedicated to simple Lie algebras, which are basically a theorist’s daily bread. The second part treats afﬁne Lie algebras and the third generalizations beyond the afﬁne case which keep appearing in various contexts in theoretical physics.1 While the topic is certainly mathematical, treating the structure theory of Lie. Representation Theory of Finite Groups and Associative Algebras - Ebook written by Charles W. Curtis, Irving Reiner. Read this book using Google Play Books app on your PC, android, iOS devices. Download for offline reading, highlight, bookmark or take notes while you read Representation Theory of Finite Groups and Associative Algebras.

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This is an introduction to the theory of affine Lie algebras and to the theory of quantum groups. It is unique in discussing these two subjects in a unified manner, which is made possible by discussing their respective applications in conformal field theory.5/5(1).

This is an introduction to the theory of affine Lie Algebras, to the theory of quantum groups, and to the interrelationships between these two fields that are encountered in conformal field theory.

Preview this book»4/5(1). Affine Lie Algebras and Quantum Groups: An Introduction, with Applications in Conformal Field Theory Jürgen Fuchs This is an introduction to the theory of affine Lie algebras, to the theory of quantum groups, and to the interrelationships between these two fields that are encountered in conformal field theory.

Find helpful customer reviews and review ratings for Affine Lie Algebras and Quantum Groups: An Introduction, with Applications in Conformal Field Theory (Cambridge Monographs on Mathematical Physics) at Read honest and 5/5(1). Semisimple Lie algebras; 2. Affine Lie algebras; 3.

WZW theories; 4. Quantum groups; 5. Duality, fusion rules, and modular invariance; Bibliography; Index. Get this from a library. Affine Lie algebras and quantum groups: an introduction, with applications in conformal field theory. [Jürgen Fuchs] -- This is an introduction to the theory of affine Lie algebras, to the theory of quantum groups, and to the interrelationships between these two fields that are encountered in conformal field theory.

Affine Lie algebras and quantum groups: an introduction, with applications in conformal field theory. [Jürgen Fuchs] This book describes the theory of semi simple and affine Lie algebras, and of quantum groups.

Various applications of these theories to two-dimensional conformal field theories are presented. an introduction, with. 4 Quantum groups Hopf algebras Deformations of enveloping algebras Representation theory Quantum dimensions The truncated Kronecker product R-matrices Quantized groups Affine Lie algebras and quantum groups Literature 5 Duality, fusion rules, and modular invariance This is an introduction to the theory of affine Lie algebras, to the theory of quantum groups, and to the interrelationships between these two fields that are encountered in conformal field theory.

The description of affine algebras covers the classification problem, the connection with loop algebras, and representation theory including modular properties. The necessary background from the. What is a good reference for a fast approach to construct affine Kac-Moody algebras from finite-dimensional simple Lie algebras.

I know that Kac's book and many others do a very detailed and progressive construction, but I mean a understandable and direct realization as in the Hong and Kang's book about Quantum groups. Abstract. This chapter is a basic introduction to affine Lie algebras, preparing the stage for their application to conformal field theory.

In Sect. after having introduced the affine Lie algebras per se, we show how the fundamental concepts of roots, weights, Cartan matrices, and Weyl groups are extended to the affine by: Abstract. The first important results in the theory of representations of infinite-dimensional Lie groups were obtained in the book by Friedrichs “Mathematical problems of quantum field theory” (), which inspired whole series of papers on automorphisms of the commutation by: The book contains several well-written, accessible survey papers in many interrelated areas of current research.

These areas cover various aspects of the representation theory of Lie algebras, finite groups of Lie types, Hecke algebras, and Lie superalgebras. There is a book by Kumar ("Kac-Moody groups, their flag varieties, and representation theory") that does the construction for the Stack Exchange Network Stack Exchange network consists of Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

In Pure and Applied Mathematics, One special feature of the representation theory of affine Lie algebras is the role of certain generating functions, which correspond in the geometric interpretation to δ-function loops, and which are known in the physics literature as quantum fields.

Though these generating functions do not strictly speaking belong to the. The quantum groups discussed in this book are the quantized enveloping algebras introduced by Drinfeld and Jimbo inor variations thereof. The theory of quantum groups has led to a new, extremely rigid structure, in which the objects of the theory are provided with canonical basis with rather remarkable properties.

David Kazhdan, George Lusztig; Affine Lie algebras and quantum groups, International Mathematics Research Notices, VolumeIssue 2, 1 JanuaryPagesCited by: Sell Affine Lie Algebras and Quantum Groups, by Fuchs - ISBN - Ship for free.

- Bookbyte. This is an introduction to the theory of affine Lie algebras, to the theory of quantum groups, and to the interrelationships between these two fields that are encountered in conformal field theory.

The description of affine algebras covers the classification problem, the connection with loop algebras, and representation theory including modular.

Lie groups and quantum algebras are connected through their common universal enveloping algebra. The adjoint action of Lie group on its algebra is naturally extended to related q.

Lusztig's quantum group. Tilting modules. The Fusion Category in Action. Lecture Affine Lie algebras. The fusion ring. Lecture Kashiwara Crystals.

Crystal bases and quantum groups. Crystals of tableaux. A peek at tableau combinatorics. Exercises. There are exercises at the last page in Lectures 2,3,4,5 and 9. Recommended texts.Affine quantum groups are certain pseudo-quasitriangular Hopf algebras that arise in mathematical physics in the context of integrable quantum field .Additional Sources for Math Book Reviews; About MAA Reviews; Mathematical Communication; Information for Libraries; Author Resources; Advertise with MAA; Meetings.

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