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Author: Jürgen Fuchs
Publisher: Cambridge University Press
Published: 1995-03-09
Total Pages: 452
ISBN-13: 9780521484121
DOWNLOAD EBOOKThis 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.
Author: Toshiaki Shoji
Publisher: American Mathematical Society(RI)
Published: 2004
Total Pages: 514
ISBN-13:
DOWNLOAD EBOOKA collection of research and survey papers written by speakers at the Mathematical Society of Japan's 10th International Conference. This title presents an overview of developments in representation theory of algebraic groups and quantum groups. It includes papers containing results concerning Lusztig's conjecture on cells in affine Weyl groups.
Author: Roger William Carter
Publisher: Cambridge University Press
Published: 2005-10-27
Total Pages: 662
ISBN-13: 9780521851381
DOWNLOAD EBOOKThis book provides a thorough but relaxed mathematical treatment of Lie algebras.
Author: Jacob Greenstein
Publisher: Birkhäuser
Published: 2023-03-12
Total Pages: 0
ISBN-13: 9783030638511
DOWNLOAD EBOOKThis volume collects chapters that examine representation theory as connected with affine Lie algebras and their quantum analogues, in celebration of the impact Vyjayanthi Chari has had on this area. The opening chapters are based on mini-courses given at the conference “Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification”, held on the occasion of Chari’s 60th birthday at the Catholic University of America in Washington D.C., June 2018. The chapters that follow present a broad view of the area, featuring surveys, original research, and an overview of Vyjayanthi Chari’s significant contributions. Written by distinguished experts in representation theory, a range of topics are covered, including: String diagrams and categorification Quantum affine algebras and cluster algebras Steinberg groups for Jordan pairs Dynamical quantum determinants and Pfaffians Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification will be an ideal resource for researchers in the fields of representation theory and mathematical physics.
Author: Pavel Etingof
Publisher: American Mathematical Soc.
Published: 2016-08-05
Total Pages: 362
ISBN-13: 1470434415
DOWNLOAD EBOOKIs there a vector space whose dimension is the golden ratio? Of course not—the golden ratio is not an integer! But this can happen for generalizations of vector spaces—objects of a tensor category. The theory of tensor categories is a relatively new field of mathematics that generalizes the theory of group representations. It has deep connections with many other fields, including representation theory, Hopf algebras, operator algebras, low-dimensional topology (in particular, knot theory), homotopy theory, quantum mechanics and field theory, quantum computation, theory of motives, etc. This book gives a systematic introduction to this theory and a review of its applications. While giving a detailed overview of general tensor categories, it focuses especially on the theory of finite tensor categories and fusion categories (in particular, braided and modular ones), and discusses the main results about them with proofs. In particular, it shows how the main properties of finite-dimensional Hopf algebras may be derived from the theory of tensor categories. Many important results are presented as a sequence of exercises, which makes the book valuable for students and suitable for graduate courses. Many applications, connections to other areas, additional results, and references are discussed at the end of each chapter.
Author: Jürgen Fuchs
Publisher: Cambridge University Press
Published: 2003-10-07
Total Pages: 464
ISBN-13: 9780521541190
DOWNLOAD EBOOKThis book gives an introduction to Lie algebras and their representations. Lie algebras have many applications in mathematics and physics, and any physicist or applied mathematician must nowadays be well acquainted with them.
Author: Christian Kassel
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 540
ISBN-13: 1461207835
DOWNLOAD EBOOKHere is an introduction to the theory of quantum groups with emphasis on the spectacular connections with knot theory and Drinfeld's recent fundamental contributions. It presents the quantum groups attached to SL2 as well as the basic concepts of the theory of Hopf algebras. Coverage also focuses on Hopf algebras that produce solutions of the Yang-Baxter equation and provides an account of Drinfeld's elegant treatment of the monodromy of the Knizhnik-Zamolodchikov equations.
Author: Molin Ge
Publisher: World Scientific Publishing Company
Published: 2016-02-16
Total Pages: 596
ISBN-13: 9814340960
DOWNLOAD EBOOKThis unique volume summarizes with a historical perspective several of the major scientific achievements of Ludwig Faddeev, with a foreword by Nobel Laureate C N Yang. The volume that spans over fifty years of Faddeev's career begins where he started his own scientific research, in the subject of scattering theory and the three-body problem. It then continues to describe Faddeev's contributions to automorphic functions, followed by an extensive account of his many fundamental contributions to quantum field theory including his original article on ghosts with Popov. Faddeev's contributions to soliton theory and integrable models are then described, followed by a survey of his work on quantum groups. The final scientific section is devoted to Faddeev's contemporary research including articles on his long-term interest in constructing knotted solitons and understanding confinement. The volume concludes with his personal view on science and mathematical physics in particular.
Author: Cisar Gómez
Publisher: Cambridge University Press
Published: 1996-04-18
Total Pages: 477
ISBN-13: 0521460654
DOWNLOAD EBOOKA 1996 introduction to integrability and conformal field theory in two dimensions using quantum groups.
Author: Vyjayanthi Chari
Publisher: Cambridge University Press
Published: 1995-07-27
Total Pages: 672
ISBN-13: 9780521558846
DOWNLOAD EBOOKSince they first arose in the 1970s and early 1980s, quantum groups have proved to be of great interest to mathematicians and theoretical physicists. The theory of quantum groups is now well established as a fascinating chapter of representation theory, and has thrown new light on many different topics, notably low-dimensional topology and conformal field theory. The goal of this book is to give a comprehensive view of quantum groups and their applications. The authors build on a self-contained account of the foundations of the subject and go on to treat the more advanced aspects concisely and with detailed references to the literature. Thus this book can serve both as an introduction for the newcomer, and as a guide for the more experienced reader. All who have an interest in the subject will welcome this unique treatment of quantum groups.
