a group. In particular, \_[\_1,\_1]{}\_[\_2,\_2]{}\_[\_1+\_2,\_1+\_2]{}, which means that we cannot decompose $\Phi_{\lambda,\Omega}$ as in the case of a two–parameter group of diffeomorphisms. The Taylor expansion of the pull–back of $\Phi_{\lambda,\Omega}$ is formally given by \^\*\_[,]{} T= \_[k,k’=0]{}\^ \_. \[Taylorfamily\] Since the diffeomorphisms $\Phi_{\lambda,\Omega}$ do not form a group we cannot write this expansion directly in terms of Lie derivatives as in the previous case, Eq. (\[Taylorgroup\]). Nevertheless, in order to study the characteristics and properties of the gauge transformations to be derived in Section \[gaugeiandt\], we would like to find an alternative way of expressing the expansion (\[Taylorfamily\]) in terms of suitable Lie derivatives, in a similar way as it was done in [@BMMS; @BS] in the one–parameter case. To this end, new objects called [*knight diffeomorphisms*]{} were introduced in [@BMMS; @BS]. Broadly speaking, they are a composition of one-parameter groups of diffeomorphisms that can reproduce the action of a given family of diffeomorphisms, in such a way that the more groups we compose the better the approximation is. When the number of composed groups tends to infinity the reproduction of the family is exact (see [@BMMS; @SB; @BS] for a detailed account on knight diffeomorphisms). The main aim for 