Quantum Isometry Groups / Infosys Science Foundation Series (PDF)
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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.
He has received numerous awards and academic recognitions for his work, which include Shanti Swarup Bhatnagar Award (2012), J.C. Bose National Fellowship (2016), Swarnajayanthi Fellowship (2009), B.M. Birla Science Prize (2006), the INSA Medal for Young Scientists (2004), the Junior Associateship of I.C.T.P. (Italy) for 2003-07 and the Alexander von Humboldt Fellowship for 2000-01. He has been elected Fellow of the Indian Academy of Sciences (Bangalore) in the year 2015. He has visited several universities and institutes in India and abroad, including Massachusetts Institute of Technology (Cambridge), University of California (Berkeley), Max Planck Institute for Mathematics (Bonn), The Fields Institute (Canada), The Instituto Nacional de Matemática Pura e Aplicada (Brazil), University of Lancaster (England), and The Institute for Research in Fundamental Science (Iran), and delivered invited lectures at many conferences and workshops all over the world.
JYOTISHMAN BHOWMICK
- Autoren: Debashish Goswami , Jyotishman Bhowmick
- 2017, 1st ed. 2016, 235 Seiten, Englisch
- Verlag: Springer-Verlag GmbH
- ISBN-10: 813223667X
- ISBN-13: 9788132236672
- Erscheinungsdatum: 05.01.2017
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“The book gives an up-to date of the results of an analogue of the group of isometries in the framework of noncommutative geometry and quantum groups. A unique feature of this book is the emphasis on the interaction of C-star algebraic compact quantum groups … .The book is an interesting book for the researchers working in this area which is still ‘hot’ enough. The physical motivations and possible applications given in this book are more interesting examples.” (Ahmed Hegazi, zbMATH 1381.81004, 2018)
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