Do Killing–Yano tensors form a Lie algebra?

Authors

David Kastor, University of Massachusetts - AmherstFollow
Sourya Ray, University of Massachusetts - Amherst
Jennie Traschen, University of Massachusetts - AmherstFollow

Publication Date

2007

Journal or Book Title

Classical and Quantum Gravity

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 Poincaré and (A)dS symmetry algebras.

Comments

This is the pre-published version harvested from ArXiv. The published version is located at http://iopscience.iop.org/0264-9381/24/14/014/

Pages

3759-

Volume

24

Issue

14

Recommended Citation

Kastor, David; Ray, Sourya; and Traschen, Jennie, "Do Killing–Yano tensors form a Lie algebra?" (2007). Classical and Quantum Gravity. 1235.
Retrieved from https://scholarworks.umass.edu/physics_faculty_pubs/1235