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Field name	Details
Dewey Class	514.74
Title	Quantum Isometry Groups ([EBook]) / by Debashish Goswami, Jyotishman Bhowmick.
Author	Goswami, Debashish
Added Personal Name	Bhowmick, Jyotishman author.
Other name(s)	SpringerLink (Online service)
Publication	New Delhi : : Springer India : : Imprint: Springer, , 2016.
Physical Details	XXVIII, 235 p. : online resource.
Series	Infosys Science Foundation Series 2363-6149
ISBN	9788132236672
Summary Note	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.:
Contents note	Chapter 1. Introduction -- Chapter 2. Preliminaries -- Chapter 3. Classical and Noncommutative Geometry -- Chapter 4. Definition and Existence of Quantum Isometry Groups -- Chapter 5. Quantum Isometry Groups of Classical and Quantum -- Chapter 6. Quantum Isometry Groups of Discrete Quantum Spaces -- Chapter 7. Nonexistence of Genuine Smooth CQG Actions on Classical Connected Manifolds -- Chapter 8. Deformation of Spectral Triples and Their Quantum Isometry Groups -- Chapter 9. More Examples and Computations -- Chapter 10. Spectral Triples and Quantum Isometry Groups on Group C*-Algebras.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-81-322-3667-2
Links to Related Works	Subject References: Differential Geometry . Functional Analysis . Global Analysis and Analysis on Manifolds . Global analysis (Mathematics) . Manifolds (Mathematics) . Mathematical Physics . Mathematics . Quantum Physics . Authors: Bhowmick, Jyotishman . Goswami, Debashish . Corporate Authors: SpringerLink (Online service) . Series: Infosys Science Foundation Series . Classification: 514.74 .

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Quantum Isometry Groups

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