  We study possible restrictions on the structure of curvature corrections to
gravitational theories in the context of their corresponding Kac--Moody
algebras, following the initial work on E10 in Class. Quant. Grav. 22 (2005)
2849. We first emphasize that the leading quantum corrections of M-theory can
be naturally interpreted in terms of (non-gravity) fundamental weights of E10.
We then heuristically explore the extent to which this remark can be
generalized to all over-extended algebras by determining which curvature
corrections are compatible with their weight structure, and by comparing these
curvature terms with known results on the quantum corrections for the
corresponding gravitational theories.
