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

TL;DR

This paper explores the algebraic structure of conformal Killing-Yano forms in geometries with skew-symmetric torsion, revealing conditions under which these forms form a graded Lie algebra, especially in special geometric settings.

Contribution

It introduces a graded Lie algebra structure for conformal Killing-Yano forms with torsion and identifies conditions for its existence in specific geometric contexts.

Findings

Graded Lie algebra structure for torsionful conformal Killing-Yano forms.

Existence of algebraic structure on constant curvature and Einstein manifolds.

Extension of the structure to generalized geometry and hidden symmetries.

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.