Do Killing-Yano tensors form a Lie Algebra?

Kastor, David; Ray, Sourya; Traschen, Jennie

Do Killing-Yano tensors form a Lie Algebra?

Authors

Kastor, David

Ray, Sourya

Traschen, Jennie

Description

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.
17 pages