Formulation of supersymmetry on a lattice as a representation of a deformed superalgebra

The lattice superalgebra of the link approach is shown to satisfy a Hopf algebraic supersymmetry where the difference operators are introduced as momentum operators. The violation of the Leibniz rule for the lattice difference operators is interpreted as the coproduct structure of a (quasi)triangular Hopf algebra and the associated field theory is consistently defined as a braided quantum field theory. An algebraic formulation of the path integral is defined perturbatively and the corresponding Ward-Takahashi identities can be derived on the lattice. The claimed inconsistency of the link approach related to an ordering ambiguity for the product of fields is solved by introducing an almost trivial braiding structure corresponding to the triangular structure of the Hopf algebraic superalgebra. This can be seen as a generalization of the spin-statistics relation on the lattice. For the consistency of this braiding structure of fields a grading of the momentum operator is required.