Lie algebra of conformal Killing-Yano forms
arXiv:1603.06338 · doi:10.1088/0264-9381/33/12/125033
Abstract
We provide a generalization of the Lie algebra of conformal Killing vector fields to conformal Killing-Yano forms. A new Lie bracket for conformal Killing-Yano forms that corresponds to slightly modified Schouten-Nijenhuis bracket of differential forms is proposed. We show that conformal Killing-Yano forms satisfy a graded Lie algebra in constant curvature manifolds. It is also proven that normal conformal Killing-Yano forms in Einstein manifolds also satisfy a graded Lie algebra. The constructed graded Lie algebras reduce to the graded Lie algebra of Killing-Yano forms and the Lie algebras of conformal Killing and Killing vector fields in special cases.
arXiv comment8 pages, published version
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- Harmonic spinors from twistors and potential forms
- Symmetries of modified Dirac operators in supergravity flux backgrounds
- Algebra structure of conformal Killing-Yano forms in geometries with skew-symmetric torsion