Affine Lie Algebras and Quantum Groups PDF Download
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Author: Jürgen Fuchs
Publisher: Cambridge University Press
ISBN: 9780521484121
Category : Mathematics
Languages : en
Pages : 452
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Book Description
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.
Author: Jürgen Fuchs
Publisher: Cambridge University Press
ISBN: 9780521484121
Category : Mathematics
Languages : en
Pages : 452
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Book Description
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.
Author: Toshiaki Shoji
Publisher: American Mathematical Society(RI)
ISBN:
Category : Computers
Languages : en
Pages : 514
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Book Description
A 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
ISBN: 9780521851381
Category : Mathematics
Languages : en
Pages : 662
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Book Description
This book provides a thorough but relaxed mathematical treatment of Lie algebras.
Author: Jürgen Fuchs
Publisher: Cambridge University Press
ISBN: 9780521541190
Category : Mathematics
Languages : en
Pages : 464
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Book Description
This 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: Pavel Etingof
Publisher: American Mathematical Soc.
ISBN: 1470434415
Category : Mathematics
Languages : en
Pages : 362
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Book Description
Is 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: Molin Ge
Publisher: World Scientific Publishing Company
ISBN: 9814340960
Category : Science
Languages : en
Pages : 596
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Book Description
This 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: Christian Kassel
Publisher: Springer Science & Business Media
ISBN: 1461207835
Category : Mathematics
Languages : en
Pages : 540
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Book Description
Here 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: Cisar Gómez
Publisher: Cambridge University Press
ISBN: 0521460654
Category : Mathematics
Languages : en
Pages : 477
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Book Description
A 1996 introduction to integrability and conformal field theory in two dimensions using quantum groups.
Author: Vyjayanthi Chari
Publisher: Cambridge University Press
ISBN: 9780521558846
Category : Mathematics
Languages : en
Pages : 672
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Book Description
Since 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.
Author: Bangming Deng
Publisher: American Mathematical Soc.
ISBN: 0821841866
Category : Mathematics
Languages : en
Pages : 790
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Book Description
"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. More precisely, it investigates the Ringel-Hall algebra realization for the positive part of a quantum enveloping algebra associated with a symmetrizable Cartan matrix and it looks closely at the Beilinson-Lusztig-MacPherson realization for the entire quantum $\mathfrak{gl}_n$. The book begins with the two realizations of generalized Cartan matrices, namely, the graph realization and the root datum realization. From there, it develops the representation theory of quivers with automorphisms and the theory of quantum enveloping algebras associated with Kac-Moody Lie algebras. These two independent theories eventually meet in Part 4, under the umbrella of Ringel-Hall algebras. Cartan matrices can also be used to define an important class of groups--Coxeter groups--and their associated Hecke algebras. Hecke algebras associated with symmetric groups give rise to an interesting class of quasi-hereditary algebras, the quantum Schur algebras. The structure of these finite dimensional algebras is used in Part 5 to build the entire quantum $\mathfrak{gl}_n$ through a completion process of a limit algebra (the Beilinson-Lusztig-MacPherson algebra). The book is suitable for advanced graduate students. Each chapter concludes with a series of exercises, ranging from the routine to sketches of proofs of recent results from the current literature."--Publisher's website.
