Coproduct and star product in field theories on Lie-algebra noncommutative space-times

We propose a new approach to field theory on {κ}-Minkowski noncommutative space-time, a popular example of Lie-algebra space-time. Our proposal is essentially based on the introduction of a star product, a technique which is proving to be very fruitful in analogous studies of canonical noncommutative space-times, such as the ones recently found to play a role in the description of certain string-theory backgrounds. We find to be incorrect the expectation, previously reported in the literature, that the lack of symmetry of the {κ}-Poincar\'e coproduct should lead to interaction vertices that are not symmetric under exchanges of the momenta of identical particles entering the relevant processes. We show that in {κ}-Minkowski the coproduct and the star product must indeed treat momenta in a nonsymmetric way, but the overall structure of interaction vertices is symmetric under exchange of identical particles. We also show that in {κ}-Minkowski field theories it is convenient to introduce the concepts of ``planar'' and ``nonplanar'' Feynman loop diagrams, again in close analogy with the corresponding concepts previously introduced in the study of field theories in canonical noncommutative space-times.