Do Killing–Yano tensors form a Lie algebra?Classical and Quantum Gravity
AbstractKilling–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 Poincaré and (A)dS symmetry algebras.
Citation InformationDavid Kastor, Sourya Ray and Jennie Traschen. "Do Killing–Yano tensors form a Lie algebra?" Classical and Quantum Gravity Vol. 24 Iss. 14 (2007)
Available at: http://works.bepress.com/david_kastor/21/