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Mathematics of the USSR-Izvestiya, 1975, Volume 9, Issue 5, Pages 939–949
DOI: https://doi.org/10.1070/IM1975v009n05ABEH001512
(Mi im2075)
 

This article is cited in 7 scientific papers (total in 7 papers)

Complex homogeneous spaces of semisimple Lie groups of the first category

F. M. Malyshev
References:
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 M~. If G is a linear group, then the manifolds M are homogeneous domains in M~; moreover the fibers of the Tits fibration of 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.
Received: 09.01.1975
Bibliographic databases:
UDC: 519.4
MSC: 32M10
Language: English
Original paper language: Russian
Citation: F. M. Malyshev, “Complex homogeneous spaces of semisimple Lie groups of the first category”, 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 Math. USSR-Izv.
\yr 1975
\vol 9
\issue 5
\pages 939--949
\mathnet{http://mi.mathnet.ru/eng/im2075}
\crossref{https://doi.org/10.1070/IM1975v009n05ABEH001512}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=402132}
\zmath{https://zbmath.org/?q=an:0322.53024}
Linking options:
  • https://www.mathnet.ru/eng/im2075
  • https://doi.org/10.1070/IM1975v009n05ABEH001512
  • https://www.mathnet.ru/eng/im/v39/i5/p992
  • This publication is cited in the following 7 articles:
    1. 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
    2. Dmitri Akhiezer, Progress in Mathematics, 306, Lie Groups: Structure, Actions, and Representations, 2013, 1  crossref
    3. Giuliana Gigante, “Hyperbolicity outside a compact set and homogeneous spaces”, Annali di Matematica, 176:1 (1999), 73  crossref  mathscinet  zmath
    4. Giuliana Gigante, Giuseppe Tomassini, “CR-structures on a real Lie algebra”, Advances in Mathematics, 94:1 (1992), 67  crossref
    5. 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
    6. F. M. Malyshev, “Complex homogeneous spaces of semisimple Lie groups of type Dn”, Math. USSR-Izv., 11:4 (1977), 783–805  mathnet  crossref  mathscinet  zmath
    7. 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
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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    Abstract page:296
    Russian version PDF:87
    English version PDF:12
    References:59
    First page:1
     
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