The loop algebra of quantum gravity

Certain topological aspects of the space of the classical T-observables as well as that of the space of quantum T-operators in the loop representation of quantum gravity will be analysed in some detail. It will be shown that the space of classical T-observables can be imbedded in a linear extension that admits a suitable equivalence relation such that the resulting quotient space supports a non-unital Hopf algebra structure. Finally, the classical loop phase space for general relativity will be constructed explicitly and a number of unusual features noted.