Quantum SL(3,C)'s with classical representation theory

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We study and classify almost all quantum SL(3,C)'s whose representation theory is ``similar'' to that of the (ordinary) group SL(3,C). Only one case, related to smooth elliptic curves, could not be treated completely.
27 pages, LaTeX2e and AMS-LaTeX 1.2, no figures; minor rewriting and typos corrected

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