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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Simply transitive groups and Kähler structures on homogeneous Siegel domains
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by Josef Dorfmeister PDF
Trans. Amer. Math. Soc. 288 (1985), 293-305 Request permission

Abstract:

We determine the Lie algebras of all simply transitive groups of automorphisms of a homogeneous Siegel domain $D$ as modifications of standard normal $j$-algebras. We show that the Lie algebra of all automorphisms of $D$ is a "complete isometry algebra in standard position". This implies that $D$ carries a riemannian metric $\tilde g$ with nonpositive sectional curvature satisfying Lie $\operatorname {Iso}(D,\tilde g) = \operatorname {Lie}\; \operatorname {Aut} \text {D}$. We determine all Kähler metrics $f$ on $D$ for which the group $\operatorname {Aut}(D,f)$ of holomorphic isometries acts transitively. We prove that in this case $\operatorname {Aut}(D,f)$ contains a simply transitive split solvable subgroup. The results of this paper are used to prove the fundamental conjecture for homogeneous Kähler manifolds admitting a solvable transitive group of automorphisms.
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Additional Information
  • © Copyright 1985 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 288 (1985), 293-305
  • MSC: Primary 32M10; Secondary 53C55
  • DOI: https://doi.org/10.1090/S0002-9947-1985-0773062-6
  • MathSciNet review: 773062