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Lie Group Actions in Complex Analysis / by Dimitrij Akhiezer

データ種別 電子書籍
版 1st ed. 1995.
出版者 Wiesbaden : Vieweg+Teubner Verlag : Imprint: Vieweg+Teubner Verlag
出版年 1995

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URL オンライン

EB2016642


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書誌ID OB01019400
本文言語 英語
一般注記 1 Lie theory -- 1.1 Complex spaces -- 1.2 Lie group actions -- 1.3 One-parameter transformation groups -- 1.4 Vector fields -- 1 5 Infinitesimal transformations -- 1.6 Analyticity of Lie group actions -- 1.7 Lie homomorphism -- 1.8 Global actions -- 2 Automorphism groups -- 2.1 Topology in Hol(X, Y) -- 2.2 Local linearization of a compact group with a fixed point -- 2.3 The automorphism group of a compact complex space -- 2.4 Automorphisms of fiber bundles -- 2.5 Proper actions -- 2.6 The automorphism group of a bounded domain -- 2.7 The automorphism groups of the polydisk and the ball -- 2.8 A characterization of the ball -- 2.9 Bounded domains with compact quotient D/Aut(D) -- 3 Compact homogeneous manifolds -- 3.1 Flag manifolds -- 3.2 Equivariant projective embeddings -- 3.3 Automorphism groups of flag manifolds -- 3.4 Parallelizable manifolds -- 3.5 Tits fibration -- 3.6 Manifolds fibered by tori -- 3.7 The role of the fundamental group -- 3.8 An estimate of the dimension of Aut(X) -- 3.9 Compact homogeneous Kähler manifolds -- 4 Homogeneous vector bundles -- 4.1 Coherent analytic G-sheaves -- 4.2 Holomorphic vector G-bundles -- 4.3 Theorem of R.Bott. Proof of the Borel-Weil theorem -- 4.4 Application of the Leray spectral sequence -- 4.5 Proof of the theorem of R.Bott -- 4.6 Invertible sheaves on G/P for P maximal parabolic -- 4.7 Computations in root systems -- 4.8 Cohomology of the tangent sheaf -- 5 Function theory on homogeneous manifolds -- 5.1 Representations of compact Lie groups on Fréchet spaces -- 5.2 Differentiable vectors and Fourier series in O(X) -- 5.3 Reductive complex Lie groups -- 5.4 Quasi-affine homogeneous varieties -- 5.5 Holomorphically separable homogeneous manifolds -- 5.6 Stein homogeneous manifolds -- 5.7 Observable subgroups -- 5.8 Invariant plurisubharmonic functions and geodesic convexity -- Concluding remarks -- Index of notations -- Index of terminology.
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Summary: 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
著者標目 *Akhiezer, Dimitrij
SpringerLink (Online service)
統一書名標目 Aspects of Mathematics ;
件　名 LCSH:Functions of complex variables
LCSH:Mathematical analysis
LCSH:Algebra
FREE:Functions of a Complex Variable
FREE:Analysis
FREE:Algebra
分　類 LCC:QA331.7
DC23:515.9
巻冊次 ISBN:9783322802675 RefWorks出力（各巻）
print ; ISBN:9783322802699 RefWorks出力（各巻）
print ; ISBN:9783322802682 RefWorks出力（各巻）
print ; ISBN:9783528064204 RefWorks出力（各巻）
資料種別 機械可読データファイル
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