An Introduction to the Noncommutative Sphere and some Extensions

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This is a copy of the talk given at the conference ``Methods in Field Theory'' at Stara Lesna, The Slovak Republic, Sepemeber 22-26, 1997. An introduction to the noncommutative sphere and a summary of the results of articles q-alg/9703038 Gratus5, and q-alg/9708003 Gratus6 is given. This includes results about the the algebra of scalar, spinor and vector fields on the noncommutative sphere. Possible extensions of these results including a ``Wick rotation'' to the one and two sheeted hyperboloid are also examined.