Do Killing-Yano tensors form a Lie Algebra?
arXiv:0705.0535 · doi:10.1088/0264-9381/24/14/014
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.
17 pages
References in corpus (9)
- SUSY in the sky
- Complete Integrability of Geodesic Motion in General Kerr-NUT-AdS Spacetimes
- Killing-Yano Tensors, Rank-2 Killing Tensors, and Conserved Quantities in Higher Dimensions
- Hidden Symmetry of Higher Dimensional Kerr-NUT-AdS Spacetimes
- The first law of black brane mechanics
- Conserved gravitational charges from Yano tensors
- Gravitational charges of transverse asymptotically AdS spacetimes
- Hamiltonians for Reduced Gravity
- Positivity Bounds for the Y-ADM Mass Density
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- Killing-Yano Forms of a Class of Spherically Symmetric Space-Times II: A Unified Generation of Higher Forms
- Algebra structure of conformal Killing-Yano forms in geometries with skew-symmetric torsion
- Rigidity of Killing-Yano and conformal Killing-Yano superalgebras