An Invitation to Quantum Groups and Duality - 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 An Invitation to Quantum Groups and Duality write by Thomas Timmermann. This book was released on 2008. An Invitation to Quantum Groups and Duality available in PDF, EPUB and Kindle. This book provides an introduction to the theory of quantum groups with emphasis on their duality and on the setting of operator algebras. Part I of the text presents the basic theory of Hopf algebras, Van Daele's duality theory of algebraic quantum groups, and Woronowicz's compact quantum groups, staying in a purely algebraic setting. Part II focuses on quantum groups in the setting of operator algebras. Woronowicz's compact quantum groups are treated in the setting of $C^*$-algebras, and the fundamental multiplicative unitaries of Baaj and Skandalis are studied in detail. An outline of Kustermans' and Vaes' comprehensive theory of locally compact quantum groups completes this part. Part III leads to selected topics, such as coactions, Baaj-Skandalis-duality, and approaches to quantum groupoids in the setting of operator algebras. The book is addressed to graduate students and non-experts from other fields. Only basic knowledge of (multi-) linear algebra is required for the first part, while the second and third part assume some familiarity with Hilbert spaces, $C^*$-algebras, and von Neumann algebras.
Quantum Isometry Groups
Quantum Isometry 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 Isometry Groups write by Debashish Goswami. This book was released on 2017-01-05. Quantum Isometry Groups available in PDF, EPUB and Kindle. This book offers an up-to-date overview of the recently proposed theory of quantum isometry groups. Written by the founders, it is the first book to present the research on the “quantum isometry group”, highlighting the interaction of noncommutative geometry and quantum groups, which is a noncommutative generalization of the notion of group of isometry of a classical Riemannian manifold. The motivation for this generalization is the importance of isometry groups in both mathematics and physics. The framework consists of Alain Connes’ “noncommutative geometry” and the operator-algebraic theory of “quantum groups”. The authors prove the existence of quantum isometry group for noncommutative manifolds given by spectral triples under mild conditions and discuss a number of methods for computing them. One of the most striking and profound findings is the non-existence of non-classical quantum isometry groups for arbitrary classical connected compact manifolds and, by using this, the authors explicitly describe quantum isometry groups of most of the noncommutative manifolds studied in the literature. Some physical motivations and possible applications are also discussed.
Compact Matrix Quantum Groups and Their Combinatorics
Compact Matrix Quantum Groups and Their Combinatorics - 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 Matrix Quantum Groups and Their Combinatorics write by Amaury Freslon. This book was released on 2023-07-27. Compact Matrix Quantum Groups and Their Combinatorics available in PDF, EPUB and Kindle.
Quantum Field Theory III: Gauge Theory
Quantum Field Theory III: Gauge 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 Field Theory III: Gauge Theory write by Eberhard Zeidler. This book was released on 2011-08-17. Quantum Field Theory III: Gauge Theory available in PDF, EPUB and Kindle. In this third volume of his modern introduction to quantum field theory, Eberhard Zeidler examines the mathematical and physical aspects of gauge theory as a principle tool for describing the four fundamental forces which act in the universe: gravitative, electromagnetic, weak interaction and strong interaction. Volume III concentrates on the classical aspects of gauge theory, describing the four fundamental forces by the curvature of appropriate fiber bundles. This must be supplemented by the crucial, but elusive quantization procedure. The book is arranged in four sections, devoted to realizing the universal principle force equals curvature: Part I: The Euclidean Manifold as a Paradigm Part II: Ariadne's Thread in Gauge Theory Part III: Einstein's Theory of Special Relativity Part IV: Ariadne's Thread in Cohomology For students of mathematics the book is designed to demonstrate that detailed knowledge of the physical background helps to reveal interesting interrelationships among diverse mathematical topics. Physics students will be exposed to a fairly advanced mathematics, beyond the level covered in the typical physics curriculum. Quantum Field Theory builds a bridge between mathematicians and physicists, based on challenging questions about the fundamental forces in the universe (macrocosmos), and in the world of elementary particles (microcosmos).
Analysis and Quantum Groups
Analysis and 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 Analysis and Quantum Groups write by Lars Tuset. This book was released on 2022-07-27. Analysis and Quantum Groups available in PDF, EPUB and Kindle. This volume presents a completely self-contained introduction to the elaborate theory of locally compact quantum groups, bringing the reader to the frontiers of present-day research. The exposition includes a substantial amount of material on functional analysis and operator algebras, subjects which in themselves have become increasingly important with the advent of quantum information theory. In particular, the rather unfamiliar modular theory of weights plays a crucial role in the theory, due to the presence of ‘Haar integrals’ on locally compact quantum groups, and is thus treated quite extensively The topics covered are developed independently, and each can serve either as a separate course in its own right or as part of a broader course on locally compact quantum groups. The second part of the book covers crossed products of coactions, their relation to subfactors and other types of natural products such as cocycle bicrossed products, quantum doubles and doublecrossed products. Induced corepresentations, Galois objects and deformations of coactions by cocycles are also treated. Each section is followed by a generous supply of exercises. To complete the book, an appendix is provided on topology, measure theory and complex function theory.
