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On the Spectra of Quantum Groups

2014-04-07 Mathematics
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Release : 2014-04-07
Genre : Mathematics
Kind : eBook
Book Rating : 74X/5 ( reviews)

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Book Synopsis On the Spectra of Quantum Groups by : Milen Yakimov

Download or read book On the Spectra of Quantum Groups written by Milen Yakimov. This book was released on 2014-04-07. Available in PDF, EPUB and Kindle. Book excerpt: Joseph and Hodges-Levasseur (in the A case) described the spectra of all quantum function algebras on simple algebraic groups in terms of the centers of certain localizations of quotients of by torus invariant prime ideals, or equivalently in terms of orbits of finite groups. These centers were only known up to finite extensions. The author determines the centers explicitly under the general conditions that the deformation parameter is not a root of unity and without any restriction on the characteristic of the ground field. From it he deduces a more explicit description of all prime ideals of than the previously known ones and an explicit parametrization of .

Quantum Groups and Their Representations

2012-12-06 Science
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Release : 2012-12-06
Genre : Science
Kind : eBook
Book Rating : 965/5 ( reviews)

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Book Synopsis Quantum Groups and Their Representations by : Anatoli Klimyk

Download or read book Quantum Groups and Their Representations written by Anatoli Klimyk. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Introduction to Quantum Groups

1996 Science
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Release : 1996
Genre : Science
Kind : eBook
Book Rating : 237/5 ( reviews)

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Book Synopsis Introduction to Quantum Groups by : Masud Chaichian

Download or read book Introduction to Quantum Groups written by Masud Chaichian. This book was released on 1996. Available in PDF, EPUB and Kindle. Book excerpt: In the past decade there has been an extemely rapid growth in the interest and development of quantum group theory.This book provides students and researchers with a practical introduction to the principal ideas of quantum groups theory and its applications to quantum mechanical and modern field theory problems. It begins with a review of, and introduction to, the mathematical aspects of quantum deformation of classical groups, Lie algebras and related objects (algebras of functions on spaces, differential and integral calculi). In the subsequent chapters the richness of mathematical structure and power of the quantum deformation methods and non-commutative geometry is illustrated on the different examples starting from the simplest quantum mechanical system — harmonic oscillator and ending with actual problems of modern field theory, such as the attempts to construct lattice-like regularization consistent with space-time Poincaré symmetry and to incorporate Higgs fields in the general geometrical frame of gauge theories. Graduate students and researchers studying the problems of quantum field theory, particle physics and mathematical aspects of quantum symmetries will find the book of interest.

Quantum Groups and Their Applications in Physics

1996 Science
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Release : 1996
Genre : Science
Kind : eBook
Book Rating : 472/5 ( reviews)

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Book Synopsis Quantum Groups and Their Applications in Physics by : Leonardo Castellani

Download or read book Quantum Groups and Their Applications in Physics written by Leonardo Castellani. This book was released on 1996. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on quantum groups, i.e., continuous deformations of Lie groups, and their applications in physics. These algebraic structures have been studied in the last decade by a growing number of mathematicians and physicists, and are found to underlie many physical systems of interest. They do provide, in fact, a sort of common algebraic ground for seemingly very different physical problems. As it has happened for supersymmetry, the q-group symmetries are bound to play a vital role in physics, even in fundamental theories like gauge theory or gravity. In fact q-symmetry can be considered itself as a generalization of supersymmetry, evident in the q-commutator formulation. The hope that field theories on q-groups are naturally reguralized begins to appear founded, and opens new perspectives for quantum gravity. The topics covered in this book include: conformal field theories and quantum groups, gauge theories of quantum groups, anyons, differential calculus on quantum groups and non-commutative geometry, poisson algebras, 2-dimensional statistical models, (2+1) quantum gravity, quantum groups and lattice physics, inhomogeneous q-groups, q-Poincaregroup and deformed gravity and gauging of W-algebras.

Lectures on Quantum Groups

2002 Mathematical physics
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Release : 2002
Genre : Mathematical physics
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis Lectures on Quantum Groups by : Pavel I. Etingof

Download or read book Lectures on Quantum Groups written by Pavel I. Etingof. This book was released on 2002. Available in PDF, EPUB and Kindle. Book excerpt: Based on lectures given at Harvard University in 1997, this book is an introduction to the theory of quantum groups and its development between 1982 and 1997. Topics covered include: relevant quasiclassical objects; bialgebras; Hopf algebras; and lie associators.

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