Symmetry operators of Killing spinors and superalgebras in AdS_5

Abstract

We construct the first-order symmetry operators of Killing spinor equation in terms of odd Killing-Yano forms. By modifying the Schouten-Nijenhuis bracket of Killing-Yano forms, we show that the symmetry operators of Killing spinors close into an algebra in AdS_5 spacetime. Since the symmetry operator algebra of Killing spinors corresponds to a Jacobi identity in extended Killing superalgebras, we investigate the possible extensions of Killing superalgebras to include higher-degree Killing-Yano forms. We found that there is a superalgebra extension but no Lie superalgebra extension of the Killing superalgebra constructed out of Killing spinors and odd Killing-Yano forms in AdS_5 background.

13 pages

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• Do Killing-Yano tensors form a Lie Algebra?
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Cited by in corpus (8)

• Lie algebra of conformal Killing-Yano forms
• Twistor spinors and extended conformal superalgebras
• Gauged twistor spinors and symmetry operators
• Hidden symmetries and Lie algebra structures from geometric and supergravity Killing spinors
• Generalized symmetry superalgebras
• Extended superalgebras from twistor and Killing spinors
• Algebra structure of conformal Killing-Yano forms in geometries with skew-symmetric torsion
• Non-compact manifolds with Killing spinors