We determine the space of commuting symmetries of the Laplace operator on pseudo-Riemannian manifolds of constant curvature and derive its algebra structure. Our construction is based on Riemannian tractor calculus, allowing us to construct a prolongation of the differential system for symmetric Killing tensors. We also discuss some aspects of its relation to projective differential geometry.
"Prolongation of symmetric Killing tensors and commuting symmetries of the Laplace operator." Rocky Mountain J. Math. 47 (2) 587 - 619, 2017. https://doi.org/10.1216/RMJ-2017-47-2-587