Principal Bundles: The Quantum Case by Stephen Bruce SontzPrincipal Bundles: The Quantum Case by Stephen Bruce Sontz

Principal Bundles: The Quantum Case

byStephen Bruce Sontz

Paperback | April 30, 2015

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This introductory text is the first book about quantum principal bundles and their quantum connections which are natural generalizations to non-commutative geometry of principal bundles and their connections in differential geometry. To make for a more self-contained book there is also much background material on Hopf algebras, (covariant) differential calculi, braid groups and compatible conjugation operations. The approach is slow paced and intuitive in order to provide researchers and students in both mathematics and physics ready access to the material.

Stephen Bruce Sontz is a Professor at Centro de Investigacion en Matematicas (CIMAT). He received his Ph.D. from the University of Virginia, USA, in 1994.
Title:Principal Bundles: The Quantum CaseFormat:PaperbackDimensions:350 pagesPublished:April 30, 2015Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3319158287

ISBN - 13:9783319158280

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Table of Contents

Introduction.- First Order Differential Calculus.- Fodc's of a Hopf Algebra.- Adjoint Co-action.- Covariant Bimodules.- Covariant Fodc's.- The Braid Groups.- An Interlude: Some Abstract Nonsense.- The Braided Exterior Algebra.- Higher Order Differential Calculus.- Structures.- Quantum Principal Bundles.- Finite Classical Groups.- Dunkl Operators as Covariant Derivatives in a QPB.- What Next?.

Editorial Reviews

"The book contains a lot of exercises of different degree of difficulties, but the proofs of the theorems are done in detail. The book is very elaborate and very welcome not only for graduate students, but also for all people interested in mathematical physics." (Stefan Berceanu, zbMATH 1358.58002, 2017)