Many texts give a simple form of Emmy Noether's conservation theorem: Each one-parameter group of symmetries of a Lagrangian system gives a conserved quantity of that system. It is a beautiful result and entirely clear -- once you are shown the proof.
But Noether proved two more involved versions of the theorem: Any finite dimensional Lie gorup action that preserves a Lagrangian gives some kind of family of conserved quantities that I do not yet understand, and an infinite-dimensional Lie group gives something more complicated that I do not yet understand.
Several sources claim that the difference between the finite- and infinite-dimensional versions says something important about the failure of momentum-energy conservation in General Relativity.
Can anyone explain what they mean, or point me to sources?
Actually, I don't see how either version can say anything definitive about failure of conservation, since each seems to give sufficient but NOT necessary conditions for conservation of a quantity.