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arXiv · 0705.0535

Do Killing-Yano tensors form a Lie Algebra?

David Kastor·Sourya Ray·Jennie Traschen
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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.

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David Kastor, Sourya Ray, Jennie Traschen. 2007-05-03. Do Killing-Yano tensors form a Lie Algebra?. https://doi.org/10.1088/0264-9381%2F24%2F14%2F014

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