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The automorphism groups of compact homogeneous spaces

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Abstract

Considering the automorphism groups of compact homogeneous spaces we inspect certain general properties, indicate a method for calculating the groups, and illustrate it with examples in a few particular cases.

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References

  1. Onishchik A. L., Topology of Transitive Transformation Groups, Johann Ambrosius Barth, Leipzig; Berlin; Heidelberg (1994).

    MATH  Google Scholar 

  2. Bredon G. E., Introduction to Compact Transformation Groups, Academic Press, New York; London (1972).

    MATH  Google Scholar 

  3. Vinberg E. B., Gorbatsevich V. V., and Shvartsman O. V., “Discrete subgroups of Lie groups,” in: Contemporary Problems of Mathematics. Fundamental Trends. Vol. 41 (Itogi Nauki i Tekhniki) [in Russian], VINITI, Moscow, 1988, pp. 5–120.

    MathSciNet  MATH  Google Scholar 

  4. Kargapolov M. I. and Merzlyakov Yu. I., Fundamentals of the Theory of Groups, Springer-Verlag, New York; Heidelberg; Berlin (1979).

    Book  MATH  Google Scholar 

  5. Gorbatsevich V. V., “Modifications of transitive actions of Lie groups on compact manifolds and some of their applications,” in: Problems of the Theory of Groups and Homological Algebra [in Russian], Yaroslavsk. Univ., Yaroslavl, 1981, pp. 131–145.

    Google Scholar 

  6. Gorbatsevich V. V., “On compact homogeneous spaces with a solvable fundamental group,” I: Geometric methods in problems of analysis and algebra, 1981, pp. 71–87; II: Problems of the theory of groups and homological algebra. 1982, pp. 13–28; III: Problems of the theory of groups and homological algebra, 1985, pp. 93–103; IV: Problems of the theory of groups and homological algebra, 1991, pp. 88–98.

    Google Scholar 

  7. Gorbatsevich V. V. and Onishchik A. L., “Lie transformation groups,” in: Lie Groups and Lie Algebras I. Foundations of Lie Theory. Lie Transformation Groups., Encycl. Math. Sci., 20, 95–229 (1993).

    MathSciNet  MATH  Google Scholar 

  8. Greenleaf F. and Moskovitz M., “Compactness of homogeneous spaces of finite volume,” Amer. J. Math., 97, 248–259 (1975).

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Moscow State Technological University, Moscow, Russia

    V. V. Gorbatsevich

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  1. V. V. Gorbatsevich
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Correspondence to V. V. Gorbatsevich.

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Original Russian Text Copyright © 2016 Gorbatsevich V. V.

Moscow. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 57, No. 4, pp. 721–745, July–August, 2016; DOI: 10.17377/smzh.2016.57.401. Original article submitted July 15, 2015.

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Gorbatsevich, V.V. The automorphism groups of compact homogeneous spaces. Sib Math J 57, 565–581 (2016). https://doi.org/10.1134/S0037446616040017

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  • DOI: https://doi.org/10.1134/S0037446616040017

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