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Lie Group Actions in Complex Analysis

  • Dmitri N. Akhiezer

Part of the Aspects of Mathematics book series (ASMA, volume 27)

Table of contents

  1. Front Matter
    Pages i-vii
  2. Dmitri N. Akhiezer
    Pages 1-2
  3. Dmitri N. Akhiezer
    Pages 3-30
  4. Dmitri N. Akhiezer
    Pages 31-62
  5. Dmitri N. Akhiezer
    Pages 63-104
  6. Dmitri N. Akhiezer
    Pages 105-134
  7. Dmitri N. Akhiezer
    Pages 135-180
  8. Dmitri N. Akhiezer
    Pages 181-185
  9. Back Matter
    Pages 186-204

About this book

Introduction

This book was planned as an introduction to a vast area, where many contri­ butions have been made in recent years. The choice of material is based on my understanding of the role of Lie groups in complex analysis. On the one hand, they appear as the automorphism groups of certain complex spaces, e. g. , bounded domains in en or compact spaces, and are therefore important as being one of their invariants. On the other hand, complex Lie groups and, more generally, homoge­ neous complex manifolds, serve as a proving ground, where it is often possible to accomplish a task and get an explicit answer. One good example of this kind is the theory of homogeneous vector bundles over flag manifolds. Another example is the way the global analytic properties of homogeneous manifolds are translated into algebraic language. It is my pleasant duty to thank A. L. Onishchik, who first introduced me to the theory of Lie groups more than 25 years ago. I am greatly indebted to him and to E. B. Vinberg for the help and advice they have given me for years. I would like to express my gratitude to M. Brion, B. GilIigan, P. Heinzner, A. Hu­ kleberry, and E. Oeljeklaus for valuable discussions of various subjects treated here. A part of this book was written during my stay at the Ruhr-Universitat Bochum in 1993. I thank the Deutsche Forschungsgemeinschaft for its research support and the colleagues in Bochum for their hospitality.

Keywords

Algebra Automorphism groups Compact homogeneous manifolds Complex analysis Function theory on homogeneous manifolds Homogeneous vector bundles Theory

Authors and affiliations

  • Dmitri N. Akhiezer
    • 1
  1. 1.MoskauRussia

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-322-80267-5
  • Copyright Information Vieweg+Teubner Verlag | Springer Fachmedien Wiesbaden GmbH, Wiesbaden 1995
  • Publisher Name Vieweg+Teubner Verlag
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-322-80269-9
  • Online ISBN 978-3-322-80267-5
  • Series Print ISSN 0179-2156
  • Buy this book on publisher's site