Do Killing-Yano tensors form a Lie Algebra?
High Energy Physics - Theory
2008-11-26 v1
Abstract
Killing-Yano tensors are natural generalizations of Killing vectors. We investigate whether Killing-Yano tensors form a graded Lie algebra with respect to the Schouten-Nijenhuis bracket. We find that this proposition does not hold in general, but that it does hold for constant curvature spacetimes. We also show that Minkowski and (anti)-deSitter spacetimes have the maximal number of Killing-Yano tensors of each rank and that the algebras of these tensors under the SN bracket are relatively simple extensions of the Poincare and (A)dS symmetry algebras.
Cite
@article{arxiv.0705.0535,
title = {Do Killing-Yano tensors form a Lie Algebra?},
author = {David Kastor and Sourya Ray and Jennie Traschen},
journal= {arXiv preprint arXiv:0705.0535},
year = {2008}
}