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(2,C))->A(SL_q(2))->A(F), q^3=1, is studied as a finite quantum group symmetry of the matrix algebra M(3,C), describing the color sector of Alain Connes' formulation of the Standard Model. The duality with the Hopf algebra H,investigated in a recent work by Robert Coquereaux, is established and used to define a representation of H on M(3,C) and two commuting representations of H on A(F).