In this paper we describe the subject of automorphism groups of domains in complex space. This has been an active area of research for fifty years or more, and continues to be dynamic and developing today. We discuss noncompact automorphism groups, the Bun Wong/Rosay theorem, the Greene/Krantz conjecture, semicontinuity of automorphism groups, the method of scaling, and other current topics. Contributions from geometers, Lie theorists, analysts, and function theorists are described.

中文翻译：

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复杂分析中的自同构小组动作

在本文中，我们描述了复杂空间中域的同构群的主题。五十多年来，它一直是活跃的研究领域，并且在今天一直活跃和发展。我们讨论了非紧致自同构群，Bong Wong / Rosay定理，Greene / Krantz猜想，自同构群的半连续性，缩放方法以及其他当前主题。描述了几何学家，李理论家，分析家和功能理论家的贡献。