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OverviewThis 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. Full Product DetailsAuthor: Lars TusetPublisher: Springer International Publishing AG Imprint: Springer International Publishing AG Edition: 1st ed. 2022 Weight: 1.130kg ISBN: 9783031072451ISBN 10: 3031072456 Pages: 633 Publication Date: 28 July 2022 Audience: Professional and scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: Manufactured on demand  We will order this item for you from a manufactured on demand supplier. Table of ContentsPreface.- Set theoretic preliminaries.- Banach spaces.- Bases in Banach spaces.- Operators on Hilbert spaces.- Spectral theory.- States and representations.- Types of von Neumann algebras.- Tensor products.- Unbounded operators.- Tomita-Takesaki theory.- Spectra and type III factors.- Quantum groups and duality.- Special cases.- Classical crossed products.- Crossed products for quantum groups.- Generalized and continuous crossed products.- Basic construction and quantum groups.- Galois objects and cocycle deformations.- Doublecrossed products of quantum groups.- Induction.-Appendix.- Bibliography.- Index.- Exercises.ReviewsAuthor InformationLars Tuset is Professor of Mathematics at Oslo Metropolitan University. He has worked actively in the area of operator algebras and quantum groups since locally compact quantum groups were introduced in the 90’s, and offers firsthand experience of the development of the theory with all its pros and cons. He has previously published a monograph on compact quantum groups and their representation categories. His research includes amenability of locally compact quantum groups, and cocycle deformations of coactions of locally compact quantum groups in the context of crossed products. Tab Content 6Author Website:Countries AvailableAll regions |
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