Compact Quantum Groups and Their Representation Categories - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Compact Quantum Groups and Their Representation Categories write by Sergey Neshveyev. This book was released on 2013. Compact Quantum Groups and Their Representation Categories available in PDF, EPUB and Kindle. The book provides an introduction to the theory of compact quantum groups, emphasizing the role of the categorical point of view in constructing and analyzing concrete examples. The general theory is developed in the first two chapters and is illustrated with a detailed analysis of free orthogonal quantum groups and the Drinfeld-Jimbo $q$-deformations of compact semisimple Lie groups. The next two chapters are more specialized and concentrate on the Drinfeld-Kohno theorem, presented from the operator algebraic point of view. This book should be accessible to students with a basic knowledge of operator algebras and semisimple Lie groups.
Complex Semisimple Quantum Groups and Representation Theory
Complex Semisimple Quantum Groups and Representation Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Complex Semisimple Quantum Groups and Representation Theory write by Christian Voigt. This book was released on 2020-09-24. Complex Semisimple Quantum Groups and Representation Theory available 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.
Quantum Groups, Quantum Categories and Quantum Field Theory
Quantum Groups, Quantum Categories and Quantum Field Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Quantum Groups, Quantum Categories and Quantum Field Theory write by Jürg Fröhlich. This book was released on 2006-11-15. Quantum Groups, Quantum Categories and Quantum Field Theory available in PDF, EPUB and Kindle. This book reviews recent results on low-dimensional quantum field theories and their connection with quantum group theory and the theory of braided, balanced tensor categories. It presents detailed, mathematically precise introductions to these subjects and then continues with new results. Among the main results are a detailed analysis of the representation theory of U (sl ), for q a primitive root of unity, and a semi-simple quotient thereof, a classfication of braided tensor categories generated by an object of q-dimension less than two, and an application of these results to the theory of sectors in algebraic quantum field theory. This clarifies the notion of "quantized symmetries" in quantum fieldtheory. The reader is expected to be familiar with basic notions and resultsin algebra. The book is intended for research mathematicians, mathematical physicists and graduate students.
Quantum Groups and Their Representations
Quantum Groups and Their Representations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Quantum Groups and Their Representations write by Anatoli Klimyk. This book was released on 2012-12-06. Quantum Groups and Their Representations available 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.
Quantum Groups
Quantum Groups - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Quantum Groups write by Christian Kassel. This book was released on 2012-12-06. Quantum Groups available 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.
