The gravitationally lensed Lyman-alpha emitting galaxy, HCM6A, detected by Hu et al. (2002) at z=6.56 behind the Abell 370 cluster was observed with the MAMBO-2 array of bolometers at 1.2mm wavelength. The galaxy was not detected down to 1.08 mJy (3 sigma), but the depth of the observations and the lens amplification allow us to improve by approximately one order of magnitude previously published upper limits on far infrared emission of Lyman-alpha emitting galaxies at this redshift. The following upper limits are derived from our observations assuming typical dust parameters: dust mass <5.3x10^7 Msun, IR luminosity <2.1x10^{11} Lsun, and star formation rate, SFR<35 Msun/yr. The observed restframe UV--optical--IR spectral energy distribution (SED) of this galaxy is compatible with that of normal spiral galaxies or blue compact dwarf galaxies. SEDs of prototypical ULIRGs, such as Arp 220, are clearly excluded. Finally, we obtain an upper limit of < 2.1x10^{-2} Msun/yr/Mpc^{-3} for the dust-obscured SFR density of Lyman-alpha selected galaxies at z~6.6.
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