Khovanov-Rozansky $\mathfrak{sl}_{N}$-Homology for Periodic Links

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.