  For an $m$-periodic link $L$, we show that the Khovanov-Rozansky
$\mathfrak{sl}_N$-homology carries an action of the group $\mathbb{Z}_m$. As an
example of applications, we prove an analog of the periodicity criterion of
Borodzik--Politarczyk using $\mathfrak{sl}_N$-homology instead of Khovanov
homology.
