Exceptional ℤ₂ × ℤ₂-symmetric spaces

Andreas Kollross

Vol. 242 (2009), No. 1, 113–130

DOI: 10.2140/pjm.2009.242.113

Abstract

The notion of ℤ₂ × ℤ₂-symmetric spaces is a generalization of classical symmetric spaces, where the group ℤ₂ is replaced by ℤ₂ × ℤ₂. In this article, a classification is given of the ℤ₂ × ℤ₂-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 ℤ₂ × ℤ₂-gradings on the exceptional simple Lie algebras e₆, e₇, e₈, f₄, g₂ and so(8).

Keywords

exceptional ℤ₂ × ℤ₂ symmetric space, Lie algebra grading

Mathematical Subject Classification 2000

Primary: 53C30, 53C35

Secondary: 17B40

Milestones

Received: 3 August 2008

Accepted: 22 January 2009

Published: 1 September 2009