Hopf Algebras And Quantum Groups
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Author |
: Stefaan Caenepeel |
Publisher |
: CRC Press |
Total Pages |
: 328 |
Release |
: 2019-05-07 |
ISBN-10 |
: 9781482270396 |
ISBN-13 |
: 1482270390 |
Rating |
: 4/5 (96 Downloads) |
Synopsis Hopf Algebras and Quantum Groups by : Stefaan Caenepeel
This volume is based on the proceedings of the Hopf-Algebras and Quantum Groups conference at the Free University of Brussels, Belgium. It presents state-of-the-art papers - selected from over 65 participants representing nearly 20 countries and more than 45 lectures - on the theory of Hopf algebras, including multiplier Hopf algebras and quantum g
Author |
: Christian Kassel |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 540 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9781461207832 |
ISBN-13 |
: 1461207835 |
Rating |
: 4/5 (32 Downloads) |
Synopsis Quantum Groups by : Christian Kassel
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 |
: Thomas Timmermann |
Publisher |
: European Mathematical Society |
Total Pages |
: 436 |
Release |
: 2008 |
ISBN-10 |
: 3037190434 |
ISBN-13 |
: 9783037190432 |
Rating |
: 4/5 (34 Downloads) |
Synopsis An Invitation to Quantum Groups and Duality by : Thomas Timmermann
This book provides an introduction to the theory of quantum groups with emphasis on their duality and on the setting of operator algebras. Part I of the text presents the basic theory of Hopf algebras, Van Daele's duality theory of algebraic quantum groups, and Woronowicz's compact quantum groups, staying in a purely algebraic setting. Part II focuses on quantum groups in the setting of operator algebras. Woronowicz's compact quantum groups are treated in the setting of $C^*$-algebras, and the fundamental multiplicative unitaries of Baaj and Skandalis are studied in detail. An outline of Kustermans' and Vaes' comprehensive theory of locally compact quantum groups completes this part. Part III leads to selected topics, such as coactions, Baaj-Skandalis-duality, and approaches to quantum groupoids in the setting of operator algebras. The book is addressed to graduate students and non-experts from other fields. Only basic knowledge of (multi-) linear algebra is required for the first part, while the second and third part assume some familiarity with Hilbert spaces, $C^*$-algebras, and von Neumann algebras.
Author |
: Ken Brown |
Publisher |
: Birkhäuser |
Total Pages |
: 339 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9783034882057 |
ISBN-13 |
: 303488205X |
Rating |
: 4/5 (57 Downloads) |
Synopsis Lectures on Algebraic Quantum Groups by : Ken Brown
This book consists of an expanded set of lectures on algebraic aspects of quantum groups. It particularly concentrates on quantized coordinate rings of algebraic groups and spaces and on quantized enveloping algebras of semisimple Lie algebras. Large parts of the material are developed in full textbook style, featuring many examples and numerous exercises; other portions are discussed with sketches of proofs, while still other material is quoted without proof.
Author |
: Shahn Majid |
Publisher |
: Cambridge University Press |
Total Pages |
: 668 |
Release |
: 2000 |
ISBN-10 |
: 0521648688 |
ISBN-13 |
: 9780521648684 |
Rating |
: 4/5 (88 Downloads) |
Synopsis Foundations of Quantum Group Theory by : Shahn Majid
A graduate level text which systematically lays out the foundations of Quantum Groups.
Author |
: Florin Felix Nichita |
Publisher |
: MDPI |
Total Pages |
: 239 |
Release |
: 2019-01-31 |
ISBN-10 |
: 9783038973249 |
ISBN-13 |
: 3038973246 |
Rating |
: 4/5 (49 Downloads) |
Synopsis Hopf Algebras, Quantum Groups and Yang-Baxter Equations by : Florin Felix Nichita
This book is a printed edition of the Special Issue "Hopf Algebras, Quantum Groups and Yang-Baxter Equations" that was published in Axioms
Author |
: Shahn Majid |
Publisher |
: Cambridge University Press |
Total Pages |
: 183 |
Release |
: 2002-04-04 |
ISBN-10 |
: 9780521010412 |
ISBN-13 |
: 0521010411 |
Rating |
: 4/5 (12 Downloads) |
Synopsis A Quantum Groups Primer by : Shahn Majid
Self-contained introduction to quantum groups as algebraic objects, suitable as a textbook for graduate courses.
Author |
: Yuri I. Manin |
Publisher |
: Springer |
Total Pages |
: 122 |
Release |
: 2018-10-11 |
ISBN-10 |
: 9783319979878 |
ISBN-13 |
: 3319979876 |
Rating |
: 4/5 (78 Downloads) |
Synopsis Quantum Groups and Noncommutative Geometry by : Yuri I. Manin
This textbook presents the second edition of Manin's celebrated 1988 Montreal lectures, which influenced a new generation of researchers in algebra to take up the study of Hopf algebras and quantum groups. In this expanded write-up of those lectures, Manin systematically develops an approach to quantum groups as symmetry objects in noncommutative geometry in contrast to the more deformation-oriented approach due to Faddeev, Drinfeld, and others. This new edition contains an extra chapter by Theo Raedschelders and Michel Van den Bergh, surveying recent work that focuses on the representation theory of a number of bi- and Hopf algebras that were first introduced in Manin's lectures, and have since gained a lot of attention. Emphasis is placed on the Tannaka–Krein formalism, which further strengthens Manin's approach to symmetry and moduli-objects in noncommutative geometry.
Author |
: George Lusztig |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 361 |
Release |
: 2010-10-27 |
ISBN-10 |
: 9780817647179 |
ISBN-13 |
: 0817647171 |
Rating |
: 4/5 (79 Downloads) |
Synopsis Introduction to Quantum Groups by : George Lusztig
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 |
: Anatoli Klimyk |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 568 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9783642608964 |
ISBN-13 |
: 3642608965 |
Rating |
: 4/5 (64 Downloads) |
Synopsis Quantum Groups and Their Representations by : Anatoli Klimyk
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.