Lie algebra of conformal Killing-Yano forms

TL;DR

This paper generalizes the Lie algebra structure of conformal Killing vector fields to conformal Killing-Yano forms, introducing a new Lie bracket and demonstrating graded Lie algebra properties in specific geometric contexts.

Contribution

It proposes a new Lie bracket for conformal Killing-Yano forms and establishes their graded Lie algebra structure in constant curvature and Einstein manifolds.

Findings

Conformal Killing-Yano forms satisfy a graded Lie algebra in constant curvature manifolds.

Normal conformal Killing-Yano forms in Einstein manifolds also satisfy a graded Lie algebra.

The new algebra reduces to known Lie algebras of Killing-Yano forms and conformal Killing vector fields in special cases.

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.