Hidden symmetries and Killing tensors on curved spaces

Abstract

Higher order symmetries corresponding to Killing tensors are investigated. The intimate relation between Killing-Yano tensors and non-standard supersymmetries is pointed out. In the Dirac theory on curved spaces, Killing-Yano tensors generate Dirac type operators involved in interesting algebraic structures as dynamical algebras or even infinite dimensional algebras or superalgebras. The general results are applied to space-times which appear in modern studies. One presents the infinite dimensional superalgebra of Dirac type operators on the 4-dimensional Euclidean Taub-NUT space that can be seen as a twisted loop algebra. The existence of the conformal Killing-Yano tensors is investigated for some spaces with mixed Sasakian structures.

12 pages; talk presented at Group 27 Colloquium, Yerevan, Armenia, August 2008

References in corpus (7)

• Higher-Dimensional Black Holes: Hidden Symmetries and Separation of Variables
• Mixed 3-Sasakian structures and curvature
• Killing Forms on Symmetric Spaces
• Higher order first integrals of motion in a gauge covariant Hamiltonian framework
• Some constructions of almost para-hyperhermitian structures on manifolds and tangent bundles
• Infinite loop superalgebras of the Dirac theory on the Euclidean Taub-NUT space
• Superalgebras of Dirac operators on manifolds with special Killing-Yano tensors