We present constraints on the mass of warm dark matter (WDM) particles from a combined analysis of the matter power spectrum inferred from the Sloan Digital Sky Survey Lyman-alpha flux power spectrum at 2.2<z<4.2, cosmic microwave background data, and the galaxy power spectrum. We obtain a lower limit of mWDM greater than or similar to 10 keV (2sigma) if the WDM consists of sterile neutrinos and mWDM greater than or similar to 2 keV (2sigma) for early decoupled thermal relics. If we combine this bound with the constraint derived from x-ray flux observations of the Coma cluster, we find that the allowed sterile neutrino mass is approximately 10 keV (in the standard production scenario). Adding constraints based on x-ray fluxes from the Andromeda galaxy, we find that dark matter particles cannot be sterile neutrinos, unless they are produced by a nonstandard mechanism (resonant oscillations, coupling with the inflation) or get diluted by a large entropy release.