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