Complex Semisimple Quantum Groups And Representation Theory PDF Download
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| Author | : Christian Voigt |
| Publisher | : Springer Nature |
| Total Pages | : 382 |
| Release | : 2020-09-24 |
| Genre | : Mathematics |
| ISBN | : 3030524639 |
Download Complex Semisimple Quantum Groups and Representation Theory Book in PDF, ePub and Kindle
This book provides a thorough introduction to the theory of complex semisimple quantum groups, that is, Drinfeld doubles of q-deformations of compact semisimple Lie groups. The presentation is comprehensive, beginning with background information on Hopf algebras, and ending with the classification of admissible representations of the q-deformation of a complex semisimple Lie group. The main components are: - a thorough introduction to quantized universal enveloping algebras over general base fields and generic deformation parameters, including finite dimensional representation theory, the Poincaré-Birkhoff-Witt Theorem, the locally finite part, and the Harish-Chandra homomorphism, - the analytic theory of quantized complex semisimple Lie groups in terms of quantized algebras of functions and their duals, - algebraic representation theory in terms of category O, and - analytic representation theory of quantized complex semisimple groups. Given its scope, the book will be a valuable resource for both graduate students and researchers in the area of quantum groups.
| Author | : Leonid I. Korogodski |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 162 |
| Release | : 1998 |
| Genre | : Mathematics |
| ISBN | : 0821803360 |
Download Algebras of Functions on Quantum Groups: Part I Book in PDF, ePub and Kindle
The text is devoted to the study of algebras of functions on quantum groups. The book includes the theory of Poisson-Lie algebras (quasi-classical version of algebras of functions on quantum groups), a description of representations of algebras of functions and the theory of quantum Weyl groups. It can serve as a text for an introduction to the theory of quantum groups and is intended for graduate students and research mathematicians working in algebra, representation theory and mathematical physics.
| Author | : Anatoli Klimyk |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 568 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 3642608965 |
Download Quantum Groups and Their Representations Book in PDF, ePub and Kindle
This book start with an introduction to quantum groups for the beginner and continues as a textbook for graduate students in physics and in mathematics. It can also be used as a reference by more advanced readers. The authors cover a large but well-chosen variety of subjects from the theory of quantum groups (quantized universal enveloping algebras, quantized algebras of functions) and q-deformed algebras (q-oscillator algebras), their representations and corepresentations, and noncommutative differential calculus. The book is written with potential applications in physics and mathematics in mind. The basic quantum groups and quantum algebras and their representations are given in detail and accompanied by explicit formulas. A number of topics and results from the more advanced general theory are developed and discussed.
| Author | : George Lusztig |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 361 |
| Release | : 2010-10-27 |
| Genre | : Mathematics |
| ISBN | : 0817647171 |
Download Introduction to Quantum Groups Book in PDF, ePub and Kindle
The quantum groups discussed in this book are the quantized enveloping algebras introduced by Drinfeld and Jimbo in 1985, or 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. This book will be of interest to mathematicians working in the representation theory of Lie groups and Lie algebras, knot theorists and to theoretical physicists and graduate students. Since large parts of the book are independent of the theory of perverse sheaves, the book could also be used as a text book.
| Author | : Toshiaki Shoji |
| Publisher | : American Mathematical Society(RI) |
| Total Pages | : 514 |
| Release | : 2004 |
| Genre | : Computers |
| ISBN | : |
Download Representation Theory of Algebraic Groups and Quantum Groups Book in PDF, ePub and Kindle
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 | : Andrew Pressley |
| Publisher | : Cambridge University Press |
| Total Pages | : 246 |
| Release | : 2002-01-17 |
| Genre | : Mathematics |
| ISBN | : 9781139437028 |
Download Quantum Groups and Lie Theory Book in PDF, ePub and Kindle
This book comprises an overview of the material presented at the 1999 Durham Symposium on Quantum Groups and includes contributions from many of the world's leading figures in this area. It will be of interest to researchers and will also be useful as a reference text for graduate courses.
| Author | : N.Ja. Vilenkin |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 651 |
| Release | : 2013-04-18 |
| Genre | : Mathematics |
| ISBN | : 940172881X |
Download Representation of Lie Groups and Special Functions Book in PDF, ePub and Kindle
This is the last of three major volumes which present a comprehensive treatment of the theory of the main classes of special functions from the point of view of the theory of group representations. This volume deals with q-analogs of special functions, quantum groups and algebras (including Hopf algebras), and (representations of) semi-simple Lie groups. Also treated are special functions of a matrix argument, representations in the Gel'fand-Tsetlin basis, and, finally, modular forms, theta-functions and affine Lie algebras. The volume builds upon results of the previous two volumes, and presents many new results. Subscribers to the complete set of three volumes will be entitled to a discount of 15%.
| Author | : Vyjayanthi Chari |
| Publisher | : Cambridge University Press |
| Total Pages | : 672 |
| Release | : 1995-07-27 |
| Genre | : Mathematics |
| ISBN | : 9780521558846 |
Download A Guide to Quantum Groups Book in PDF, ePub and Kindle
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 | : Shahn Majid |
| Publisher | : Cambridge University Press |
| Total Pages | : 668 |
| Release | : 2000 |
| Genre | : Group theory |
| ISBN | : 9780521648684 |
Download Foundations of Quantum Group Theory Book in PDF, ePub and Kindle
A graduate level text which systematically lays out the foundations of Quantum Groups.
| Author | : Jens Carsten Jantzen |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 282 |
| Release | : 1996 |
| Genre | : Mathematics |
| ISBN | : 0821804782 |
Download Lectures on Quantum Groups Book in PDF, ePub and Kindle
The material is very well motivated ... Of the various monographs available on quantum groups, this one ... seems the most suitable for most mathematicians new to the subject ... will also be appreciated by a lot of those with considerably more experience. --Bulletin of the London Mathematical Society Since its origin, the theory of quantum groups has become one of the most fascinating topics of modern mathematics, with numerous applications to several sometimes rather disparate areas, including low-dimensional topology and mathematical physics. This book is one of the first expositions that is specifically directed to students who have no previous knowledge of the subject. The only prerequisite, in addition to standard linear algebra, is some acquaintance with the classical theory of complex semisimple Lie algebras. Starting with the quantum analog of $\mathfrak{sl}_2$, the author carefully leads the reader through all the details necessary for full understanding of the subject, particularly emphasizing similarities and differences with the classical theory. 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.
