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Tuesday, April 21, 2020 | History

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

Affine Lie Algebras and Quantum Groups

An Introduction, with Applications in Conformal Field Theory (Cambridge Monographs on Mathematical Physics)

by JГјrgen A. Fuchs

  • 355 Want to read
  • 2 Currently reading

Published by Cambridge University Press .
Written in English

    Subjects:
  • Linear algebra,
  • Theoretical methods,
  • Quantum field theory,
  • Mathematical Physics,
  • Science,
  • Mathematics,
  • Science/Mathematics,
  • Quantum groups,
  • Algebra - Linear,
  • Quantum Theory,
  • Mathematics / Algebra / Linear,
  • Science / Mathematical Physics,
  • Science-Mathematical Physics,
  • Science-Quantum Theory,
  • Lie algebras,
  • Conformal invariants

  • The Physical Object
    FormatPaperback
    Number of Pages447
    ID Numbers
    Open LibraryOL7742573M
    ISBN 10052148412X
    ISBN 109780521484121


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Affine Lie Algebras and Quantum Groups by JГјrgen A. Fuchs Download PDF EPUB FB2

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 Affine Lie Algebras and Quantum Groups book, 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.

MAA MathFest. Register Now; Registration Rates and Other Fees; Exhibitors and Sponsors; Abstracts; Mathematical Sessions. Invited Addresses; Invited Paper Sessions; Contributed Paper.

Idea. Affine Lie algebras (sometimes: current algebras) are the most important class of Kac-Moody Lie should be viewed as tangent Lie algebras to the loop groups, with a correction term which is sometimes related to quantization/quantum anomaly. These affine Lie algebras appear in quantum field theory as the current algebras in the WZW model as well as.

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 introduction to the theory of affine Lie algebras and to the theory of quantum groups succeeds in discussing the two subjects in a unified manner by covering their respective applications in Brand: Jurgen Fuchs.

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.

The interplay between finite dimensional algebras and Lie theory dates back many years. In more recent times, these interrelations have become even more strikingly apparent. This text combines, for the first time in book form, the theories of finite dimensional algebras and quantum groups. Destination page number Search scope Search Text Search scope Search Text.

Hopf Algebras, Quantum Groups and Yang-Baxter Equations by Florin Felix Nichita (ed.). Publisher: MDPI AG ISBN Number of pages: Description: Various aspects of the Yang-Baxter equation, related algebraic structures, and applications are.

AN INTRODUCTION TO AFFINE KAC-MOODY ALGEBRAS 5 3. Affine Kac-Moody algebras A natural problem is to generalize the theory of finite dimensional semi-simple Lie algebras to infinite dimensional Lie algebras.

A class of infinite dimensional Lie algebras called affine Kac-Moody algebra is of particular importance for this : David Hernandez. Modules Over Affine Lie Algebras at Critical Level and Quantum Groups by Qian Lin Submitted to the Department of Mathematics on Apin partial fulfillment of the requirements for the degree of Doctor of Philosophy Abstract There are two algebras associated to a reductive Lie algebra g: the De Concini-Kac quantum algebra and the Kac.

as representable functors from the category of k-algebras to groups; as commutative Hopf algebras over k; as groups in the category of schemes over k. All three points of view are important: the first is the most elementary and natural; the sec-ond leads to natural generalizations, for example, affine group schemes in a tensor category.

From the reviews of the French edition "This is a rich and useful volume. The material it treats has relevance well beyond the theory of Lie groups and algebras, ranging from the geometry of regular polytopes and paving problems to current work on finite simple groups having a (B,N)-pair structure, or "Tits systems".

A historical note provides a survey of the. EMS Newsletter 'The book is a very concise and nice introduction to Lie groups and Lie algebras. It seems to be well suited for a course on the subject.' Mathematical Reviews "The book is a very concise and nice introduction to Lie groups and Lie algebras.

It seems to be well suited for a course on the subject/5(4). These courses will serve as an introduction to geometric representation theory, quantum groups and combinatorial representation theory (i.e. the theory of crystal bases), the structure theory of extended affine Lie algebras and the representation theory of affine and toroidal Lie algebras.

The authors also desired their book to be as self-contained as possible. The interweaving of the deeper properties of Lie algebras and algebraic groups rests upon a vast base of algebra and geometry. The results needed are widely scattered, appearing in many different forms, having been introduced for many disparate purposes.An interesting geometric property for Lie groups is the existence of left-invariant affine structures on Lie groups, e.g., see here.

There is a bijection to so-called left-symmetric algebra structures on Lie algebras. The geometric problem thus can be reduced to .Poisson-Lie groups we study their relation to Lie-bi algebras and the classical Yang-Baxter equation.

Then we explain in detail the concept of quantization for them. As an example the quantization of sl2 is explicitly carried out. Next we show how quantum groups are related to the Yang-Baxter equation and how they can be used to solve it.