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Izv. Akad. Nauk SSSR Ser. Mat., 1975, Volume 39, Issue 5, Pages 992–1002 (Mi izv2075)  

This article is cited in 6 scientific papers (total in 6 papers)

Complex homogeneous spaces of semisimple Lie groups of the first category

F. M. Malyshev


Abstract: Let $G$ be a connected, real, semisimple Lie group of the first category. In this paper are found all the connected closed subgroups $L$ in $G$ which are such that there exists a complex structure on $M=G/L$, invariant under the action of $G$; and also a description is given of all such structures on $M$. It turns out that the complex homogeneous spaces $M$ thus obtained are covering spaces of homogeneous domains in compact complex homogeneous spaces $\widetilde M$. If $G$ is a linear group, then the manifolds $M$ are homogeneous domains in $\widetilde M$; moreover the fibers of the Tits fibration of $\widetilde M$ can only lie entirely in $M$, and the set of all fibers in $M$ forms a homogeneous domain in the base space of the corresponding Tits fibration.
Bibliography: 16 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1975, 9:5, 939–949

Bibliographic databases:

UDC: 519.4
MSC: 32M10
Received: 09.01.1975

Citation: F. M. Malyshev, “Complex homogeneous spaces of semisimple Lie groups of the first category”, Izv. Akad. Nauk SSSR Ser. Mat., 39:5 (1975), 992–1002; Math. USSR-Izv., 9:5 (1975), 939–949

Citation in format AMSBIB
\Bibitem{Mal75}
\by F.~M.~Malyshev
\paper Complex homogeneous spaces of semisimple Lie groups of the first category
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1975
\vol 39
\issue 5
\pages 992--1002
\mathnet{http://mi.mathnet.ru/izv2075}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=402132}
\zmath{https://zbmath.org/?q=an:0322.53024}
\transl
\jour Math. USSR-Izv.
\yr 1975
\vol 9
\issue 5
\pages 939--949
\crossref{https://doi.org/10.1070/IM1975v009n05ABEH001512}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. F. M. Malyshev, “Complex homogeneous spaces of the Lie group $SO(2k+1,2l+1)$”, Math. USSR-Izv., 10:4 (1976), 763–782  mathnet  crossref  mathscinet  zmath
    2. F. M. Malyshev, “Complex homogeneous spaces of semisimple Lie groups of type $D_n$”, Math. USSR-Izv., 11:4 (1977), 783–805  mathnet  crossref  mathscinet  zmath
    3. F. M. Malyshev, “Complete complex structures on homogeneous spaces of semisimple Lie groups”, Math. USSR-Izv., 15:3 (1980), 501–522  mathnet  crossref  mathscinet  zmath  isi
    4. Giuliana Gigante, Giuseppe Tomassini, “CR-structures on a real Lie algebra”, Advances in Mathematics, 94:1 (1992), 67  crossref
    5. Giuliana Gigante, “Hyperbolicity outside a compact set and homogeneous spaces”, Annali di Matematica, 176:1 (1999), 73  crossref  mathscinet  zmath
    6. Ahmadi S.R. Gilligan B., “Complexifying Lie Group Actions on Homogeneous Manifolds of Non-Compact Dimension Two”, Can. Math. Bul.-Bul. Can. Math., 57:4 (2014), 673–682  crossref  isi
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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