Pluecker-type relations for orthogonal planes
Algebraic Geometry
2015-06-26 v2 High Energy Physics - Theory
Differential Geometry
Abstract
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.
Keywords
Cite
@article{arxiv.math/0211170,
title = {Pluecker-type relations for orthogonal planes},
author = {José Figueroa-O'Farrill and George Papadopoulos},
journal= {arXiv preprint arXiv:math/0211170},
year = {2015}
}
Comments
39 pages (v2: substantial revision, 33% more material, link with n-Lie algebras)