Plucker type relations for orthogonal planes

We explore a Pluecker-type relation which occurs naturally in the study of maximally supersymmetric solutions of certain supergravity theories. This relation generalises at the same time the classical Pluecker relation and the Jacobi identity for a metric Lie algebra and coincides with the Jacobi identity of a metric n-Lie algebra. In low dimension we present evidence for a geometric characterisation of the relation in terms of middle-dimensional orthogonal planes in euclidean or lorentzian inner product spaces.

Note:

39 pages (v2: substantial revision, 33% more material, link with n-Lie algebras)

References(4)

Figures(0)

e-Print:
- math/9905090

Maximal supersymmetry in ten and eleven dimensions

Jose M. Figueroa-O'Farrill
(
- Edinburgh U.
)

e-Print:
- math/0109162

Maximally supersymmetric solutions of ten-dimensional and eleven-dimensional supergravities

- JHEP 03 (2003) 048
•
e-Print:
- hep-th/0211089
•
DOI:
- 10.1088/1126-6708/2003/03/048

A New maximally supersymmetric background of IIB superstring theory

- JHEP 01 (2002) 047
•
e-Print:
- hep-th/0110242
•
DOI:
- 10.1088/1126-6708/2002/01/047