Quantum Groups and Noncommutative Spaces: Perspectives on Quantum Geometry

✍ Scribed by Tomasz Brzeziński (auth.), Prof. Dr. Matilde Marcolli, Dr. Deepak Parashar (eds.)

• Publisher: Vieweg+Teubner Verlag
• Year: 2011
• Tongue: English
• Leaves: 246
• Edition: 1
• Category: Library

✦ Synopsis

This book is aimed at presenting different methods and perspectives in the theory of Quantum Groups, bridging between the algebraic, representation theoretic, analytic, and differential-geometric approaches. It also covers recent developments in Noncommutative Geometry, which have close relations to quantization and quantum group symmetries. The volume collects surveys by experts which originate from an acitvity at the Max-Planck-Institute for Mathematics in Bonn.

Contributions byTomasz Brzezinski, Branimir Cacic, Rita Fioresi, Rita Fioresi and Fabio Gavarini, Debashish Goswami, Christian Kassel, Avijit Mukherjee, Alfons Van Daele, Robert Wisbauer, Alessandro Zampini

The volume is aimed as introducing techniques and results on Quantum Groups and Noncommutative Geometry, in a form that is accessible to other researchers in related areas as well as to advanced graduate students.
The topics covered are of interest to both mathematicians and theoretical physicists.


Prof. Dr. Matilde Marcolli, Department of Mathematics, California Institute of Technology, Pasadena, California, USA.
Dr. Deepak Parashar, Cambridge Cancer Trials Centre and MRC Biostatistics Unit, University of Cambridge, United Kingdom.

✦ Table of Contents

Front Matter....Pages i-viii
Hopf-cyclic homology with contramodule coefficients....Pages 1-8
Moduli Spaces of Dirac Operators for Finite Spectral Triples....Pages 9-68
Tensor representations of the general linear super group....Pages 69-79
Quantum duality principle for quantum Grassmannians....Pages 80-95
Some remarks on the action of quantum isometry groups....Pages 96-103
Generic Hopf Galois extensions....Pages 104-120
Quantizing the Moduli Space of Parabolic Higgs Bundles....Pages 121-129
Locally compact quantum groups. Radford’s S 4 formula....Pages 130-145
Categorical aspects of Hopf algebras....Pages 146-163
Laplacians and gauged Laplacians on a quantum Hopf bundle....Pages 164-240

✦ Subjects

Mathematics, general