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Analysis and quantum groups

Tuset, Lars.

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Analysis and quantum groups

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Analysis and quantum groups/ by Lars Tuset.
作者:	Tuset, Lars.
出版者:	Cham :Springer International Publishing : : 2022.,
面頁冊數:	xiii, 633 p. :ill., digital ;24 cm.
內容註:	Preface -- 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.
Contained By:	Springer Nature eBook
標題:	Quantum groups. -
電子資源:	https://doi.org/10.1007/978-3-031-07246-8
ISBN:	9783031072468

Analysis and quantum groups
Tuset, Lars.

Analysis and quantum groups[electronic resource] /by Lars Tuset. - Cham :Springer International Publishing :2022. - xiii, 633 p. :ill., digital ;24 cm.

Preface -- 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.

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.

ISBN: 9783031072468

Standard No.: 10.1007/978-3-031-07246-8doiSubjects--Topical Terms:

629837
Quantum groups.

LC Class. No.: QC174.17.G7 / T87 2022

Dewey Class. No.: 530.143

Analysis and quantum groups
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505 0 $a Preface -- 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.
520 $a 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.
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650 2 4 $a Functional Analysis. $3 893943
650 2 4 $a Group Theory and Generalizations. $3 893889
650 2 4 $a Abstract Harmonic Analysis. $3 891093
650 2 4 $a Topological Groups and Lie Groups. $3 3593340
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