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The Structure of Semisimple Symmetric Spaces

Published online by Cambridge University Press:  20 November 2018

W. Rossmann
W. Rossmann*
Affiliation:
McMaster University, Hamilton, Ontario
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A semisimple symmetric space can be defined as a homogeneous space G/H, where G is a semisimple Lie group, H an open subgroup of the fixed point group of an involutive automorphism of G. These spaces can also be characterized as the affine symmetric spaces or pseudo-Riemannian symmetric spaces or symmetric spaces in the sense of Loos [4] with semisimple automorphism groups [3, 4]. The connected semisimple symmetric spaces are all known: they have been classified by Berger [2] on the basis of Cartan's classification of the Riemannian symmetric spaces. However, the list of these spaces is much too long to make a detailed case by case study feasible. In order to do analysis on semisimple symmetric spaces, for example, one needs a general structure theory, just as in the case of Riemannian symmetric spaces and semisimple Lie groups.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 31 , Issue 1 , 01 February 1979 , pp. 157 - 180
Copyright
Copyright © Canadian Mathematical Society 1979

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