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Linear isotropy group of an affine symmetric space

Author: Jun Nagasawa
Journal: Proc. Amer. Math. Soc. 33 (1972), 516-519
MSC: Primary 53C35
MathSciNet review: 0296860
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Abstract: Let K be a subgroup of the general linear group $ {\text{GL}}(n)$. The author found a necessary and sufficient condition that there exist an n-dimensional simply connected affine symmetric space M such that K coincides with the linear isotropy group of all affine automorphisms of M at some point in M.

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  • [1] É. Cartan, Leçons sur la géométrie des espaces de Riemann, 2nd. ed., Gauthier-Villars, Paris, 1946. MR 8, 602.
  • [2] Katsumi Nomizu, Invariant affine connections on homogeneous spaces, Amer. J. Math. 76 (1954), 33–65. MR 0059050,
  • [3] Shoshichi Kobayashi and Katsumi Nomizu, Foundations of differential geometry. Vol I, Interscience Publishers, a division of John Wiley & Sons, New York-London, 1963. MR 0152974
  • [4] -, Foundations of differential geometry. Vol. 2, Interscience Tracts in Pure and Appl. Math., no. 15, Interscience, New York, 1969. MR 38 #6501.
  • [5] Jun Nagasawa, On infinitesimal linear isotropy group of an affinely connected manifold, Proc. Japan Acad. 41 (1965), 553–557. MR 0200854
  • [6] Jun Nagasawa, Linear isotropy group of a symmetric space, Mem. Fac. Ed. Kumamoto Univ. Sect. 1 17 (1969), 1–2. MR 0252572

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Keywords: Linear isotropy group, affine symmetric space
Article copyright: © Copyright 1972 American Mathematical Society

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