Higher-dimensional loop algebras, non-abelian extensions and p-branes

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. ((orig.))