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) ) -→Fτ A (SLq(2) ) → πF A(F), q =e 2πi/3, 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 , investigated in a recent work by Robert Coquereaux, is established and used to define a representation of on M(3, C) and two commuting representations of on A(F). © World Scientific Publishing Company.