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JOURNALS // Matematicheskii Sbornik // Archive

Mat. Sb. (N.S.), 1969 Volume 80(122), Number 4(12), Pages 553–599 (Mi sm3643)

This article is cited in 34 papers

Decompositions of reductive Lie groups

A. L. Onishchik


Abstract: In this work we study decompositions $G=G'G''$ of reductive Lie groups $G$ into the product of Lie subgroups $G'$ and $G''$. Such decompositions are fully described in case $G'$ and $G''$ are reductive in $G$, or $G$ is simple and $G'$ and $G''$ are maximal. The results are applied to the classification of complex homogeneous spaces.
Bibliography: 21 titles.

UDC: 519.46

MSC: 22E46, 22E10, 22E60, 17B20

Received: 19.03.1969


 English version:
Mathematics of the USSR-Sbornik, 1969, 9:4, 515–554

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© Steklov Math. Inst. of RAS, 2025