| Explicit formula of holomorphic automorphism group on complex homogeneous bounded domains |
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| 作者姓名： | XU Yichao CHEN Minru & MA Songya Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China College of Mathematics and Information Sciences Henan University Kaifeng China |
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| 作者单位： | XU Yichao，CHEN Minru & MA Songya Academy of Mathematics and Systems Science，Chinese Academy of Sciences，Beijing 100080，China; College of Mathematics and Information Sciences，Henan University，Kaifeng 475001，China |
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| 摘 要： | We known that the maximal connected holomorphic automorphism group Aut (D)(0) is a semi-direct product of the triangle group T(D) and the maximal connected isotropic subgroup Iso(D)(0) of a fixed point in the complex homogeneous bounded domain D and any complex homogeneous bounded domain is holomorphic isomorphic to a normal Siegel domain D(VN,F). In this paper, we give the explicit formula of any holomorphic automorphism in T(D(VN, F)) and Iso(D(VN,F))(0), where G(0) is the unit connected component of the Lie group G.
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| 收稿时间： | 20 January 2006 |
| 修稿时间： | 24 April 2006 |
Explicit formula of holomorphic automorphism group on complex homogeneous bounded domains |
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| XU Yichao,CHEN Minru & MA Songya Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing ,China, College of Mathematics and Information Sciences,Henan University,Kaifeng ,China.Explicit formula of holomorphic automorphism group on complex homogeneous bounded domains[J].Science in China(Mathematics),2006,49(10):1392-1404. |
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| Authors: | XU Yichao CHEN Minru MA Songya |
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| Institution: | 1. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China
2. College of Mathematics and Information Sciences, Henan University, Kaifeng 475001, China |
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| Abstract: | We known that the maximal connected holomorphic automorphism group Aut (D)(0) is a semi-direct product of the triangle group T(D) and the maximal connected isotropic subgroup Iso(D)(0) of a fixed point in the complex homogeneous bounded domain D and any complex homogeneous bounded domain is holomorphic isomorphic to a normal Siegel domain D(VN,F). In this paper, we give the explicit formula of any holomorphic automorphism in T(D(VN, F)) and Iso(D(VN,F))(0), where G(0) is the unit connected component of the Lie group G. |
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| Keywords: | holomorphic automorphism group homogeneous Siegel domain normal Siegel domain complex homogeneous bounded domain |
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