Algebraic Groups And Quantum Groups
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| 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 | : Ken Brown |
| Publisher | : Birkhäuser |
| Total Pages | : 339 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 303488205X |
Download Lectures on Algebraic Quantum Groups Book in PDF, Epub and Kindle
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 | : Akihiko Gyoja |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 356 |
| Release | : 2010-11-25 |
| Genre | : Mathematics |
| ISBN | : 0817646973 |
Download Representation Theory of Algebraic Groups and Quantum Groups Book in PDF, Epub and Kindle
Invited articles by top notch experts Focus is on topics in representation theory of algebraic groups and quantum groups Of interest to graduate students and researchers in representation theory, group theory, algebraic geometry, quantum theory and math physics
| Author | : Christian Kassel |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 540 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461207835 |
Download Quantum Groups Book in PDF, Epub and Kindle
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 | : 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 | : 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 | : Brian Parshall |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 168 |
| Release | : 1991 |
| Genre | : Mathematics |
| ISBN | : 0821825011 |
Download Quantum Linear Groups Book in PDF, Epub and Kindle
We consider the theory of quantum groups as a natural abstraction of the theory of affine group schemes. After establishing the foundational results as the theory of induced representations, rational cohomology, and the Hochschild-Serre spectral sequence, we take up a detailed investigation of the quantum linear group [italic]GL[italic subscript]q([italic]n). In particular, we develop the global and infinitesimal representation theory of [italic]GL[italic subscript]q([italic]n) and its subgroups.
| Author | : Ross Street |
| Publisher | : Cambridge University Press |
| Total Pages | : 160 |
| Release | : 2007-01-18 |
| Genre | : Mathematics |
| ISBN | : 1139461443 |
Download Quantum Groups Book in PDF, Epub and Kindle
Algebra has moved well beyond the topics discussed in standard undergraduate texts on 'modern algebra'. Those books typically dealt with algebraic structures such as groups, rings and fields: still very important concepts! However Quantum Groups: A Path to Current Algebra is written for the reader at ease with at least one such structure and keen to learn algebraic concepts and techniques. A key to understanding these new developments is categorical duality. A quantum group is a vector space with structure. Part of the structure is standard: a multiplication making it an 'algebra'. Another part is not in those standard books at all: a comultiplication, which is dual to multiplication in the precise sense of category theory, making it a 'coalgebra'. While coalgebras, bialgebras and Hopf algebras have been around for half a century, the term 'quantum group', along with revolutionary new examples, was launched by Drinfel'd in 1986.
| Author | : Shahn Majid |
| Publisher | : Cambridge University Press |
| Total Pages | : 183 |
| Release | : 2002-04-04 |
| Genre | : Mathematics |
| ISBN | : 0521010411 |
Download A Quantum Groups Primer Book in PDF, Epub and Kindle
Self-contained introduction to quantum groups as algebraic objects, suitable as a textbook for graduate courses.
