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024 7 $a10.1007/978-81-322-3667-2
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035   $a(DE-He213)978-81-322-3667-2
035   $a(PPN)198342470
035   $a(EXLCZ)993710000001008957
100   $a20170105d2016      u|             0
101 0 $aeng
135   $aurcnu||||||||
181   $2rdacontent
182   $2rdamedia
183   $2rdacarrier
200 10$aQuantum Isometry Groups$b[electronic resource] /$fby Debashish Goswami, Jyotishman Bhowmick
205   $a1st ed. 2016.
210  1$aNew Delhi :$cSpringer India :$cImprint: Springer,$d2016.
215   $a1 online resource (254 pages)
225 1 $aInfosys Science Foundation Series in Mathematical Sciences,$x2364-4036
311   $a81-322-3665-3 
311   $a81-322-3667-X 
320   $aIncludes bibliographical references at the end of each chapters.
327   $aChapter 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.
330   $aThis book offers an up-to-date overview of the recently proposed theory of quantum isometry groups. Written by the founders, it is the first book to present the research on the ?quantum isometry group?, highlighting the interaction of noncommutative geometry and quantum groups, which is a noncommutative generalization of the notion of group of isometry of a classical Riemannian manifold. The motivation for this generalization is the importance of isometry groups in both mathematics and physics. The framework consists of Alain Connes? ?noncommutative geometry? and the operator-algebraic theory of ?quantum groups?. The authors prove the existence of quantum isometry group for noncommutative manifolds given by spectral triples under mild conditions and discuss a number of methods for computing them. One of the most striking and profound findings is the non-existence of non-classical quantum isometry groups for arbitrary classical connected compact manifolds and, by using this, the authors explicitly describe quantum isometry groups of most of the noncommutative manifolds studied in the literature. Some physical motivations and possible applications are also discussed.
410  0$aInfosys Science Foundation Series in Mathematical Sciences,$x2364-4036
606   $aGlobal analysis (Mathematics)
606   $aManifolds (Mathematics)
606   $aMathematical physics
606   $aDifferential geometry
606   $aFunctional analysis
606   $aQuantum physics
606   $aGlobal Analysis and Analysis on Manifolds$3https://scigraph.springernature.com/ontologies/product-market-codes/M12082
606   $aMathematical Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/M35000
606   $aDifferential Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21022
606   $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066
606   $aQuantum Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19080
615  0$aGlobal analysis (Mathematics).
615  0$aManifolds (Mathematics).
615  0$aMathematical physics.
615  0$aDifferential geometry.
615  0$aFunctional analysis.
615  0$aQuantum physics.
615 14$aGlobal Analysis and Analysis on Manifolds.
615 24$aMathematical Physics.
615 24$aDifferential Geometry.
615 24$aFunctional Analysis.
615 24$aQuantum Physics.
676   $a530.12
700   $aGoswami$b Debashish$4aut$4http://id.loc.gov/vocabulary/relators/aut$0300721
702   $aBhowmick$b Jyotishman$4aut$4http://id.loc.gov/vocabulary/relators/aut
906   $aBOOK
912   $a9910158671403321
996   $aQuantum Isometry Groups$92129505
997   $aUNINA