Algebra structure of conformal Killing-Yano forms in geometries with skew-symmetric torsion

2025/08/07 by Ertem, Ümit, Kelekçi, Özgür, Açık, Özgür
#FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2508.05117

Abstract

We consider conformal Killing-Yano 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 conformal Killing-Yano forms are found and a graded Lie bracket for conformal Killing-Yano 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 conformal Killing-Yano 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.

Citations

• Spinor bilinears and Killing-Yano forms in generalized geometry
• Ricci flow, Killing spinors, and T-duality in generalized geometry
• Einstein manifolds with skew torsion
• The Srni lectures on non-integrable geometries with torsion
• G₂-Manifolds With Parallel Characteristic Torsion
• Conformal Killing forms on Riemannian manifolds

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• Conformal Killing forms on nearly Kähler manifolds
• Torsionful Killing-Yano Forms under T-Duality: Transformation Conditions and Emergent Isometries