Quantum Groups and Noncommutative Spaces Perspectives on Quantum Geo
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 Noncommut
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Matilde Marcolli | Deepak Parashar (Eds.)
Quantum Groups and Noncommutative Spaces Perspectives on Quantum Geometry A Publication of the Max-Planck-Institute for Mathematics, Bonn
Bibliographic information published by the Deutsche Nationalbibliothek The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available in the Internet at http://dnb.d-nb.de.
Prof. Dr. Matilde Marcolli Mathematics Department California Institute of Technology 1200 E.California Blvd. Pasadena, CA 91125 USA [email protected] Prof. Dr. Klas Diederich (Series Editor) Bergische Universität Wuppertal Fachbereich Mathematik Gaußstraße 20 42119 Wuppertal Germany
Dr. Deepak Parashar University of Cambridge Cambridge Cancer Trials Centre Department of Oncology Addenbrooke's Hospital (Box 279) Hills Road Cambridge CB2 0QQ Cambridge Hub in Trials Methodology Research MRC Biostatistics Unit University Forvie Site Robinson Way Cambridge CB2 0SR UK [email protected]
[email protected]
Mathematics Subject Classification 17B37 Quantum groups (quantized enveloping algebras) and related deformations, 58B34 Noncommutative geometry (à la Connes) , 58B32 Geometry of quantum groups, 20G42 Quantum groups (quantized function algebras) and their representations, 16T05 Hopf algebras and their applications, 19D55 K-theory and homology; cyclic homology and cohomology, 81T75 Noncommutative geometry methods
1st Edition 2011 All rights reserved © Vieweg+Teubner Verlag | Springer Fachmedien Wiesbaden GmbH 2011 Editorial Office: Ulrike Schmickler-Hirzebruch Vieweg+Teubner Verlag is a brand of Springer Fachmedien. Springer Fachmedien is part of Springer Science+Business Media. www.viewegteubner.de No part of this publication may be reproduced, stored in a retrieval system or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the copyright holder. Registered and/or industrial names, trade names, trade descriptions etc. cited in this publication are part of the law for trade-mark protection and may not be used free in any form or by any means even if this is not specifically marked. Cover design: KünkelLopka Medienentwicklung, Heidelberg Printed on acid-free paper Printed in Germany ISBN 978-3-8348-1442-5
Contents Preface
vii
Hopf-cyclic homology with contramodule coefficients Tomasz Brzezinski
1
Moduli spaces of Dirac operators for finite spectral triples ´ c ´ ic ´ Branimir Ca
9
Tensor representations of the general linear supergroup Rita Fioresi
69
Quantum duality priciple for quantum Grassmanians Rita Fioresi and Fabio Gavarini
80
Some remarks on the action of quantum isometry groups Debashish Goswami
96
Generic Hopf Galois extensions Christian Kassel
104
Quantizing the moduli space of parabolic Higgs bundle Avijit Mukherjee
121
Locally compact quantum groups. Radford’s S 4 formula Alfons Van Daele
130
Categorical Aspects of Hopf Algebras Robert Wisbauer
146
Laplacians and gauged
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