Symmetries of ${\mathfrak{g}\mathfrak{l}}_N$-foams

We give an action of a Lie subalgebra of the Witt algebra on foams. This action is compatible with the ${\mathfrak{g}\mathfrak{l}}_N$-foam evaluation formula. In particular, this endows states spaces associated with ${\mathfrak{g}\mathfrak{l}}_N$-webs with an ${\mathfrak{s}\mathfrak{l}}_2$-action. When working in positive characteristic, this can be used to define a $p$-DG structure on these state spaces.