Abstract
In this chapter, the Vinberg, Gindikin, Piatetski-Shapiro theorem will be proved: A homogeneous bounded domain in ℂn is holomorphically isomorphic to a homogeneous Siegel domain (ref. 222). If the holomorphic automorphism group Aut (D) on a homogeneous bounded domain D is a real semisimple Lie group, this Theorem has been proved in Section 7.2. In this chapter, we discuss only the case of a non-semisimple Lie group Aut(D). By Theorem 3.23, we can add the indecomposable condition to the homogeneous bounded domain D. Then the Lie algebra aut (D) of the Lie group Aut (D) is an indecomposable effective proper J Lie algebra with the non-trivial radical by Chapter 2.
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© 2005 Science Press and Kluwer Academic Publishers
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(2005). Homogeneous Bounded Domains. In: Theory of Complex Homogeneous Bounded Domains. Mathematics and Its Applications, vol 569. Springer, Dordrecht. https://doi.org/10.1007/1-4020-2133-X_9
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DOI: https://doi.org/10.1007/1-4020-2133-X_9
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-2132-9
Online ISBN: 978-1-4020-2133-6
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