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Wednesday, May 13, 2020 | History

6 edition of Quantum groups and Lie theory found in the catalog.

Quantum groups and Lie theory

by LMS Durham Symposium on Quantum Groups (1999 Grey College, University of Durham)

  • 262 Want to read
  • 25 Currently reading

Published by Cambridge University Press in Cambridge, UK, New York, NY .
Written in English

    Subjects:
  • Quantum groups -- Congresses.,
  • Lie groups -- Congresses.,
  • Mathematical physics -- Congresses.

  • Edition Notes

    Statementedited by Andrew Pressley.
    GenreCongresses.
    SeriesLondon Mathematical Society lecture note series -- 290.
    ContributionsPressley, Andrew.
    Classifications
    LC ClassificationsQC20.7.G76 Q82 1999, QC20.7.G76 Q82 1999
    The Physical Object
    Paginationviii, 234 p. :
    Number of Pages234
    ID Numbers
    Open LibraryOL18171810M
    ISBN 100521010403
    LC Control Number2001043214

    Lie groups are smooth differentiable manifolds and as such can be studied using differential calculus, in contrast with the case of more general topological of the key ideas in the theory of Lie groups is to replace the global object, the group, with its local or linearized version, which Lie himself called its "infinitesimal group" and which has since become known as its Lie algebra. Get this from a library! Quantum groups and Lie theory. [Andrew Pressley;] -- This book comprises an overview of the material presented at the Durham Symposium on Quantum Groups and includes contributions from many of the world's leading figures in this area. It will be.

      The final chapters of the book describe the Kashiwara–Lusztig theory of so-called crystal (or canonical) bases in representations of complex semisimple Lie algebras. The choice of the topics and the style of exposition make Jantzen's book an excellent textbook for a one-semester course on quantum groups. • H. Weyl,“Quantum mechanics and group theory,” Z. Phys. 46 () 1. One of the original foundations of the use of symmetry in quantum mechanics • R. N. Cahn, “Semisimple Lie Algebras And Their Representations,” Menlo Park.

      In particular, the theory of “crystal bases” or “canonical bases” developed independently by M. Kashiwara and G. Lusztig provides a powerful combinatorial and geometric tool to study the representations of quantum groups. The purpose of this book is to provide an elementary introduction to the theory of quantum groups and crystal bases. In mathematics and theoretical physics, the term quantum group denotes one of a few different kinds of noncommutative algebras with additional structure. These include Drinfeld–Jimbo type quantum groups (which are quasitriangular Hopf algebras), compact matrix quantum groups (which are structures on unital separable C*-algebras), and bicrossproduct quantum groups. The term "quantum group" first .


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Quantum groups and Lie theory by LMS Durham Symposium on Quantum Groups (1999 Grey College, University of Durham) Download PDF EPUB FB2

The representation theory of quantum groups is discussed, as is the function algebra approach to quantum groups, and there is a new look at the origins of quantum groups in the theory Format: Paperback. Quantum mechanics is an extremely rich source of group representations and yet most introductory courses and texts avoid the language and concepts of representation theory as they are more suited to an advanced treatment of the subject.5/5(4).

The representation theory of quantum groups is discussed, as is the function algebra approach to quantum groups, and there is a new look at the origins of quantum groups in the theory Manufacturer: Cambridge University Press.

Following a general introduction to quantum mechanics and group theory Weyl explores the ideas of applying symmetry groups and algebra to problems of quantum mechanics. Unfortunately for today's reader, especially one who has been thoroughly exposed to quantum mechanics and group theory in a rigorous setting, Weyl's book is dated in its material and especially in its notation and by: Plus contributions which treat the construction and classification of quantum groups or the associated solutions of the quantum Yang-Baxter equation.

The representation theory of quantum groups is discussed, as is the function algebra approach to quantum groups, and there is a new look at the origins of quantum groups in the theory of. Quantum Groups and Lie Theory Andrew Pressley To take stock and to discuss the most fruitful directions for future research, many of the world's leading figures met at the Durham Symposium on Quantum Groups in the summer ofand this volume.

This text systematically presents the basics of quantum mechanics, emphasizing the role of Lie groups, Lie algebras, and their unitary representations. The mathematical structure of the subject is brought to the fore, intentionally avoiding significant overlap with material from standard physics courses in quantum mechanics and quantum field Brand: Springer International Publishing.

To take stock and to discuss the most fruitful directions for future research, many of the world's leading figures met at the Durham Symposium on Quantum Groups in the summer ofand this volume provides an excellent overview of the material presented there. It includes important surveys of both cyclotomic Hecke algebras and the dynamical Yang-Baxter equation.

Lie algebras Lie groups quantization quantum fields quantum mechanics representation theory Standard Model of particle physics unitary group representations two-state systems Lie algebra representations rotation and spin groups momentum and free particle fourier analysis and free particle Schroedinger representation Heisenberg group Poisson bracket and symplectic geometry.

LIE GROUPS IN PHYSICS1 version 25/06/07 Institute for Theoretical Physics Utrecht University Beta Faculty English version by G. ’t Hooft Original text by M.J.G.

Veltman B.Q.P.J. de Wit and G. ’t File Size: KB. Zee, Group Theory in a Nutshell for Physicists. A very readable and easygoing book developing group theory by example, spending signi cant time on nite groups and applications in quantum mechanics.

This is a good rst book to get the idea of how group theory is used in physics. Georgi, Lie File Size: 1MB. Quantum groups and Lie theory. [Andrew Pressley;] This book comprises an overview of the material presented at the Durham Symposium on Quantum Groups and includes contributions from many of the world's leading figures in this area.

# Quantum groups\/span>\n \u00A0\u00A0\u00A0\n schema. According to Drinfeld, a quantum group is the same as a Hopf algebra. This includes as special cases, the algebra of regular functions on an algebraic group and the enveloping algebra of a semisimple Lie algebra.

The qu- tum groups discussed in this book are the quantized enveloping algebras introduced by Drinfeld and Jimbo inor variations thereof.

Quantum Groups and Lie Theory by Andrew Pressley,available at Book Depository with free delivery worldwide. Quantum Groups and Lie Theory: Andrew Pressley: We use cookies to give you the best possible : Andrew Pressley. This is followed by discussions of Weil algebras, Chern--Weil theory, the quantum Weil algebra, and the cubic Dirac operator.

The applications to Lie theory include Duflo’s theorem for the case of quadratic Lie algebras, multiplets of representations, and Dirac induction. The last part of the book is an account of Kostant’s structure theory Brand: Springer-Verlag Berlin Heidelberg.

The discussion of quantum groups concentrates on deformed enveloping algebras and their representation theory, but other aspects such as R-matrices and matrix quantum groups are also dealt with. This book will be of interest to researchers and graduate students in. Quantum Theory, Groups and Representations: An Introduction Peter Woit Department of Mathematics, Columbia University [email protected] This book presents classical mechanics, quantum mechanics, and statistical mechanics in an almost completely algebraic setting, thereby introducing mathematicians, physicists, and engineers to the ideas relating classical and quantum mechanics with Lie algebras and Lie by: 8.

Quantum Theory for Mathematicians (Graduate Texts in Mathematics Book ) - Kindle edition by Hall, Brian C. Download it once and read it on your Kindle device, PC, phones or tablets. Use features like bookmarks, note taking and highlighting while reading Quantum Theory for Mathematicians (Graduate Texts in Mathematics Book )/5(10).

The theory of Quantum Groups is a rapidly developing area with numerous applications in mathematics and theoretical physics, e.g.

in link and knot invariants in topology, q-special functions, conformal field theory, quantum integrable models. 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 graduate students.

Since large parts of the book are independent of the theory of perverse sheaves, the work may also be used as a textbook.There is a book titled "Group theory and Physics" by Sternberg that covers the basics, including crystal groups, Lie groups, representations. I think it's a good introduction to the topic.

To quote a review on Amazon (albeit the only one): "This book is an excellent introduction to the use of group theory in physics, especially in crystallography, special relativity and particle physics.Quantum Theory, Groups and Representations: An Introduction Peter Woit Published November by Springer.

The Springer webpage for the book is SpringerLink page is here (if your institution is a Springer subscriber, this should give you electronic access to the book, as well as the possibility to buy a $ softcover version).