Quantum Linear Groups PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Quantum Linear Groups PDF full book. Access full book title Quantum Linear Groups by Brian Parshall. Download full books in PDF and EPUB format.
Author: Brian Parshall
Publisher: American Mathematical Soc.
ISBN: 0821825011
Category : Mathematics
Languages : en
Pages : 168
Get Book Here
Book Description
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: Brian Parshall
Publisher: American Mathematical Soc.
ISBN: 0821825011
Category : Mathematics
Languages : en
Pages : 168
Get Book Here
Book Description
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: Pavel I. Etingof
Publisher:
ISBN: 9781571462077
Category : Mathematical physics
Languages : en
Pages : 242
Get Book Here
Book Description
Author: Ross Street
Publisher: Cambridge University Press
ISBN: 1139461443
Category : Mathematics
Languages : en
Pages : 160
Get Book Here
Book Description
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: Peter Woit
Publisher: Springer
ISBN: 3319646125
Category : Science
Languages : en
Pages : 659
Get Book Here
Book Description
This text systematically presents the basics of quantum mechanics, emphasizing the role of Lie groups, Lie algebras, and their unitary representations. The mathematical structure of the subject is brought to the fore, intentionally avoiding significant overlap with material from standard physics courses in quantum mechanics and quantum field theory. The level of presentation is attractive to mathematics students looking to learn about both quantum mechanics and representation theory, while also appealing to physics students who would like to know more about the mathematics underlying the subject. This text showcases the numerous differences between typical mathematical and physical treatments of the subject. The latter portions of the book focus on central mathematical objects that occur in the Standard Model of particle physics, underlining the deep and intimate connections between mathematics and the physical world. While an elementary physics course of some kind would be helpful to the reader, no specific background in physics is assumed, making this book accessible to students with a grounding in multivariable calculus and linear algebra. Many exercises are provided to develop the reader's understanding of and facility in quantum-theoretical concepts and calculations.
Author: Jean Pierre Serre
Publisher:
ISBN:
Category :
Languages : en
Pages : 170
Get Book Here
Book Description
Author: Jens Carsten Jantzen
Publisher: American Mathematical Soc.
ISBN: 0821804782
Category : Mathematics
Languages : en
Pages : 282
Get Book Here
Book Description
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.
Author: Lawrence C Biedenharn
Publisher: World Scientific
ISBN: 9814500135
Category : Science
Languages : en
Pages : 305
Get Book Here
Book Description
Quantum groups are a generalization of the classical Lie groups and Lie algebras and provide a natural extension of the concept of symmetry fundamental to physics. This monograph is a survey of the major developments in quantum groups, using an original approach based on the fundamental concept of a tensor operator. Using this concept, properties of both the algebra and co-algebra are developed from a single uniform point of view, which is especially helpful for understanding the noncommuting co-ordinates of the quantum plane, which we interpret as elementary tensor operators. Representations of the q-deformed angular momentum group are discussed, including the case where q is a root of unity, and general results are obtained for all unitary quantum groups using the method of algebraic induction. Tensor operators are defined and discussed with examples, and a systematic treatment of the important (3j) series of operators is developed in detail. This book is a good reference for graduate students in physics and mathematics.
Author: Shahn Majid
Publisher: Cambridge University Press
ISBN: 0521010411
Category : Mathematics
Languages : en
Pages : 183
Get Book Here
Book Description
Self-contained introduction to quantum groups as algebraic objects, suitable as a textbook for graduate courses.
Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 974
Get Book Here
Book Description
Author: Christian Kassel
Publisher: Springer Science & Business Media
ISBN: 1461207835
Category : Mathematics
Languages : en
Pages : 540
Get Book Here
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.
