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Operator geometry and algebraic gravity

An algebraic formulation of general relativity is proposed. The formulation is applicable to quantum gravity and noncommutative space. To investigate quantum gravity we develop the canonical formalism of operator geometry, after reconstructing an algebraic canonical formulation on analytical dynamics. The remarkable fact is that the constraint equation and evolution equation of the gravitational system are algebraically unified. From the discussion of regularization we find the quantum correction of the semi-classical gravity is same as that already known in quantum field theory.