  We have examined the relationship between rotation and activity in 14
late-type (M6-M7) M dwarfs, using high resolution spectra taken at the Keck
Observatory and flux-calibrated spectra from the Sloan Digital Sky Survey. Most
are inactive at a spectral type where H-alpha emission has previously seen to
be very common. We used the cross-correlation technique to quantify the
rotational broadening; six of the stars in our sample have vsini>3.5 km/s.
Three of these stars do not exhibit H-alpha emission, despite rotating at
velocities where previous work has observed strong levels of magnetic field and
stellar activity. Our results suggest that rotation and activity in late-type M
dwarfs may not always be linked, and open several additional possibilities
including a rotation dependant activity threshold, or a Maunder-minimum
phenomenon in fully convective stars.
