On the finite-dimensional quantum group M-3 circle plus(M-2/1(Lambda(2)))(0)

We describe a few properties of the nonsemisimple associative algebra H = M-3 + (M-2/1(Lambda(2)))(0), where Lambda(2) is the Grassmann algebra with two generators. We show that H is not only a finite-dimensional algebra but also a (noncommutative) Hopf algebra, hence a finite-dimensional quantum group. By selecting a system of explicit generators, we show how it is related with the quantum enveloping of SLq(2) when the parameter q is a cubic root of unity. We describe its indecomposable projective representations as well as the irreducible ones. We also comment about the relation between this object and the theory of modular representation of the group St(2, F-3), i.e. the binary tetrahedral group. Finally, we briefly discuss its relation with the Lorentz group and, as already suggested by A. Connes, make a few comments about the possible use of this algebra in a modification of the Standard Model of particle physics (the unitary group of the semisimple algebra associated with H is U(3) x U(2) x U(1)).