Quantum and braided diffeomorphism groups

Details Quantum and braided diffeomorphism groups Quantum and braided diffeomorphism groups

1998-01-07

arxiv.org/abs/math/9801020v1

Mathematics

Quantum Algebra

36 pages latex with epsf (two figures, not critical)

Scientific paper

10.1016/S0393-0440(98)00016-3

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 quasitriangular and braided R-matrix versions. Among the examples, we construct the $q$-diffeomorphisms of the quantum plane $yx=qxy$, and recover the quantum matrices $M_q(2)$ as those respecting its braided group addition law.

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