Khovanov-Rozansky ${\mathfrak{s}\mathfrak{l}}_N$-homology for periodic links

For an $m$-periodic link $L$, we show that the Khovanov-Rozansky ${\mathfrak{s}\mathfrak{l}}_N$-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 ${\mathfrak{s}\mathfrak{l}}_N$-homology instead of Khovanov homology.