Yes. All Purple mattresses can be used on a slat-style bed frames.
Purple recommends that slats be no more than 2.75″ apart from one another, to ensure optimal support for the mattress.
This also helps prevent the mattress from sagging. Using the Purple mattress with an insufficient foundation / bed base can void your warranty so be sure that your slats are properly spaced upon initial setup of your new mattress.

Bed slats are budget-friendly, easy to repair in case of maintenance, and easy to install (or take down).
Traditional bed slats are wooden and can either be nailed down, rolled out and secured on a Velcro strip, or just laid flat on the base with a mattress on top.