Published January 1, 2025
| Version v1
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Algebra structure of conformal Killing-Yano forms in geometries with skew-symmetric torsion
Creators
- 1. Ankara Univ, Fac Engn, Dept Software Engn, TR-06830 Ankara, Turkiye
- 2. Univ Turkish Aeronaut Assoc, Fac Engn, Dept Basic Sci, Ankara, Turkiye
- 3. Ankara Univ, Fac Sci, Dept Phys, TR-06100 Ankara, Turkiye
Description
We consider conformal Killing-Yano (CKY) forms corresponding to the antisymmetric generalizations of conformal Killing vectors to higher degree forms in the presence of skew-symmetric torsion. Integrability conditions for torsionful CKY forms are found and a graded Lie bracket for CKY forms to constitute a graded Lie algebra structure is proposed. It is found that a graded Lie algebra structure for a special subset of torsionful CKY forms can be constructed for a closed and parallel skew-symmetric torsion on constant curvature and Einstein manifolds. Similar structure for generalized hidden symmetries defined from generalized connection in generalized geometry is also constructed.
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