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Izv. Akad. Nauk SSSR Ser. Mat., 1974, Volume 38, Issue 1, Pages 59–80 (Mi izv1892)  

This article is cited in 2 scientific papers (total in 2 papers)

Compact complex homogeneous spaces with solvable fundamental group

D. N. Akhiezer


Abstract: In this paper, complex Lie groups $G$ acting transitively and effectively on complex manifolds $X$ with solvable (nilpotent) fundamental groups are studied. It is shown that if $\pi_1(X)$ is nilpotent, then locally $G=S\times N$, where $S$ is semisimple and $N$ is nilpotent. In the case when $\pi_1(X)$ is solvable, the Levi decomposition of the group $G$ is direct if and only if the stationary subgroup contains a maximal unipotent subgroup of the semisimple part. The question of the existence of transitive semisimple groups on $X$ is considered.

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English version:
Mathematics of the USSR-Izvestiya, 1974, 8:1, 61–83

Bibliographic databases:

UDC: 513.6
MSC: Primary 57E20, 32C10; Secondary 22E10
Received: 09.11.1972

Citation: D. N. Akhiezer, “Compact complex homogeneous spaces with solvable fundamental group”, Izv. Akad. Nauk SSSR Ser. Mat., 38:1 (1974), 59–80; Math. USSR-Izv., 8:1 (1974), 61–83

Citation in format AMSBIB
\Bibitem{Akh74}
\by D.~N.~Akhiezer
\paper Compact complex homogeneous spaces with solvable fundamental group
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1974
\vol 38
\issue 1
\pages 59--80
\mathnet{http://mi.mathnet.ru/izv1892}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=340654}
\zmath{https://zbmath.org/?q=an:0309.22008}
\transl
\jour Math. USSR-Izv.
\yr 1974
\vol 8
\issue 1
\pages 61--83
\crossref{https://doi.org/10.1070/IM1974v008n01ABEH002096}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. V. Gorbatsevich, “On Lie groups, transitive on compact solvmanifolds”, Math. USSR-Izv., 11:2 (1977), 271–292  mathnet  crossref  mathscinet  zmath
    2. V. V. Gorbatsevich, “On the homotopy structure of compact complex homogeneous manifolds”, Izv. Math., 80:2 (2016), 329–341  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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