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

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.