We postulate a new type of operator algebra with a non-abelian extensi
on. This algebra generalizes the Kac-Moody algebra in string theory an
d the Mickelsson-Faddeev algebra in three dimensions to higher-dimensi
onal extended objects (p-branes). We then construct new BRST operators
, covariant derivatives and curvature tensors in the higher-dimensiona
l generalization of loop space.