A FINITE QUANTUM SYMMETRY OF M(3,C)

The 27-dimensional Hopf algebra A(F), defined by the exact sequence of quantum groups A ((SL(S, C)) -->(Fr) A (SLq(2)) -->(pi F) A(F), q = e (2 pi i/3) is studied as a finite quantum group symmetry of the matrix algebra M(3, C), describing the color sector of Alain Connes' formula tion of the Standard Model. The duality with the Hopf algebra H, inves tigated in a recent work by Robert Coquereaux, is established and used to define a representation of H on M(3, C) and two commuting represen tations of H on A(F).