New aspects of one-dimensional N = 4-extended supersymmetry

In this talk I will present very recent results concerning the N = 4-extended supersymmetry in one-dimension. The new features consist in the construction of the non-minimal linear multiplets realized by 8 bosonic and 8 fermionic components, the construction of non-linear realizations induced by the supersymmetrization of the second Hopf fibration and, finally, the construction of a new superalgebra with N = 4 fermionic generators (two of them nilpotent) obtained by the dimensional reduction of the four-dimensional twisted super-Yang-Mills theory.