Abstract
We develop a general theory of ‘quantum’ diffeomorphism groups based on the universal comeasuring quantum group M ( A) associated to an algebra A, and its various quotients. Explicit formulae are introduced for this construction, as well as dual quasi-triangular and braided R-matrix versions. Among the examples, we construct the q-diffeomorphisms of the quantum plane yx = qxy, and recover the quantum matrices M q as q-diffeomorphisms respecting its braided group addition law.
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