The generalisation: a solution for spheres of arbitrary dimension

Abstract

In Definition 0.1, a Killing tensor is a symmetric bilinear form K _αβ on the manifold M. In what follows we will interpret it in two other ways, each of which gives rise to a Lie bracket and hence to a Lie algebra generated by Killing tensors. On one hand, we can use the metric to identify the symmetric bilinear form KK _αβ with a symmetric endomorphism ${{K}^{\alpha }}_{\beta}$.