Invariant dependence structures and Archimedean copulas

We consider a family of copulas that are invariant under univariate truncation. Such a family has some distinguishing properties: it is generated by means of a univariate function; it can capture non-exchangeable dependence structures; it can be easily simulated. Moreover, such a class presents strong probabilistic similarities with the class of Archimedean copulas from a theoretical and practical point of view.