Exceptional (Z/2Z) x (Z/2Z)-symmetric spaces

Details Exceptional (Z/2Z) x (Z/2Z)-symmetric spaces Exceptional (Z/2Z) x (Z/2Z)-symmetric spaces

2008-08-03

arxiv.org/abs/0808.0306v1

Pacific J. Math. 242 (2009), no. 1, 113--130

Mathematics

Differential Geometry

13 pages

Scientific paper

10.2140/pjm.2009.242.113

The notion of (Z/2Z) x (Z/2Z)-symmetric spaces is a generalization of classical symmetric spaces, where the group Z/2Z is replaced by (Z/2Z) x (Z/2Z). In this article, a classification is given of the (Z/2Z) x (Z/2Z)-symmetric spaces G/K where G is an exceptional compact Lie group or Spin(8), complementing recent results of Bahturin and Goze. Our results are equivalent to a classification of (Z/2Z) x (Z/2Z)-gradings on the exceptional simple Lie algebras e6, e7, e8, f4, g2 and so(8).

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