  We have identified twenty-seven candidate very low mass members of the
relatively young Alpha Persei open cluster from a six square degree CCD imaging
survey. Based on their I magnitudes and the nominal age and distance to the
cluster, these objects should have masses less than 0.1 Msunif they are cluster
members. We have subsequently obtained intermediate resolution spectra of
seventeen of these objects using the Keck II telescope and LRIS spectrograph.
We have also obtained near-IR photometry for many of the stars. Our primary
goal was to determine the location of the "lithium depletion boundary" and
hence to derive a precise age for the cluster. We detect lithium with
equivalent widths greater than or equal to 0.4 \AA in five of the program
objects. We have constructed a color-magnitude diagram for the faint end of the
Alpha Persei main sequence. These data allow us to accurately determine the
Alpha Persei single-star lithium depletion boundary at M(I$_C$) = 11.47, M(Bol)
= 11.42, (R-I)$_{C0}$ = 2.12, spectral type M6.0. By reference to theoretical
evolutionary models, this converts fairly directly into an age for the Alpha
Persei cluster of 90 $\pm$ 10 Myr. At this age, the two faintest of our
spectroscopically confirmed members should be sub-stellar (i.e., brown dwarfs)
according to theoretical models.
