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Lie Group Actions in Complex Analysis

  • Book
  • © 1995

Overview

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

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Table of contents (7 chapters)

Keywords

About this book

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 forthe 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.

Authors and Affiliations

  • Moskau, Russia

    Dmitri N. Akhiezer

About the author

Prof. Dr. Dimitri Akhiezer lehrt Mathematik an einer Moskauer Universität.

Bibliographic Information

  • Book Title: Lie Group Actions in Complex Analysis

  • Authors: Dmitri N. Akhiezer

  • Series Title: Aspects of Mathematics

  • DOI: https://doi.org/10.1007/978-3-322-80267-5

  • Publisher: Vieweg+Teubner Verlag Wiesbaden

  • eBook Packages: Springer Book Archive

  • Copyright Information: Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden 1995

  • Softcover ISBN: 978-3-322-80269-9Published: 16 December 2011

  • eBook ISBN: 978-3-322-80267-5Published: 06 December 2012

  • Series ISSN: 0179-2156

  • Edition Number: 1

  • Number of Pages: VII, 204

  • Topics: Functions of a Complex Variable, Analysis, Algebra

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