Deformed Bialgebra of Diffeomorphisms

The algebra of diffeomorphisms derived from general coordinate transformations on commuting coordinates is represented by differential operators on noncommutative spaces. The algebra remains unchanged, the comultiplication however is deformed, that way we have found a deformed bialgebra of diffeomorphisms. Scalar, vector and tensor fields are defined with appropriate transformation laws under the deformed algebra and a differential calculus is developed. For pedagogical reasons the formalism is developed for the $\theta$-deformed space as it is the best known example of deformed spaces.