Differential calculus on q - Minkowski space 1

We wish to report here on a recent approach [1] to the non-commutative calculus on q-Minkowski space which is based on the reflection equations (RE) with no spectral parameter. These are considered as the expression of the invariance (under the coaction of the q-Lorentz group) of the commutation properties which define the different q-Minkowski algebras. This approach also allows us to discuss the possible ambiguities in the definition of q-Minkowski space Mq and its differential calculus. The commutation relations among the generators of Mq (coordinates), Dq (derivatives), Λq (one-forms) and a few invariant (scalar) operators are established. The correspondence of the obtained expressions with those of [2] is given in a table at the end.