Quantum Groups and Noncommutative Spaces - 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 Noncommutative Spaces write by Matilde Marcolli. This book was released on 2010-11-02. Quantum Groups and Noncommutative Spaces available in PDF, EPUB and Kindle. This book is aimed at presenting different methods and perspectives in the theory of Quantum Groups, bridging between the algebraic, representation theoretic, analytic, and differential-geometric approaches. It also covers recent developments in Noncommutative Geometry, which have close relations to quantization and quantum group symmetries. The volume collects surveys by experts which originate from an acitvity at the Max-Planck-Institute for Mathematics in Bonn.
Quantum Groups and Noncommutative Geometry
Quantum Groups and Noncommutative Geometry - 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 Noncommutative Geometry write by Yuri I. Manin. This book was released on 2018-10-11. Quantum Groups and Noncommutative Geometry available in PDF, EPUB and Kindle. 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.
Noncommutative Spacetimes
Noncommutative Spacetimes - 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 Noncommutative Spacetimes write by Paolo Aschieri. This book was released on 2009-07-14. Noncommutative Spacetimes available in PDF, EPUB and Kindle. There are many approaches to noncommutative geometry and to its use in physics. This volume addresses the subject by combining the deformation quantization approach, based on the notion of star-product, and the deformed quantum symmetries methods, based on the theory of quantum groups. The aim of this work is to give an introduction to this topic and to prepare the reader to enter the research field quickly. The order of the chapters is "physics first": the mathematics follows from the physical motivations (e.g. gauge field theories) in order to strengthen the physical intuition. The new mathematical tools, in turn, are used to explore further physical insights. A last chapter has been added to briefly trace Julius Wess' (1934-2007) seminal work in the field.
Noncommutative Spacetimes
Noncommutative Spacetimes - 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 Noncommutative Spacetimes write by Paolo Aschieri. This book was released on 2009-08-29. Noncommutative Spacetimes available in PDF, EPUB and Kindle. There are many approaches to noncommutative geometry and its use in physics, the ? operator algebra and C -algebra one, the deformation quantization one, the qu- tum group one, and the matrix algebra/fuzzy geometry one. This volume introduces and develops the subject by presenting in particular the ideas and methods recently pursued by Julius Wess and his group. These methods combine the deformation quantization approach based on the - tion of star product and the deformed (quantum) symmetries methods based on the theory of quantum groups. The merging of these two techniques has proven very fruitful in order to formulate ?eld theories on noncommutative spaces. The aim of the book is to give an introduction to these topics and to prepare the reader to enter the research ?eld himself/herself. This has developed from the constant interest of Prof. W. Beiglboeck, editor of LNP, in this project, and from the authors experience in conferences and schools on the subject, especially from their interaction with students and young researchers. In fact quite a few chapters in the book were written with a double purpose, on the one hand as contributions for school or conference proceedings and on the other handaschaptersforthepresentbook.Thesearenowharmonizedandcomplemented by a couple of contributions that have been written to provide a wider background, to widen the scope, and to underline the power of our methods.
Introduction to Quantum Groups
Introduction to 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 Introduction to Quantum Groups write by Masud Chaichian. This book was released on 1996. Introduction to Quantum Groups available in PDF, EPUB and Kindle. 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.
