  We explore the prospects for confining alkaline-earth Rydberg atoms in an
optical lattice via optical dressing of the secondary core valence electron.
Focussing on the particular case of strontium, we identify experimentally
accessible magic wavelengths for simultaneous trapping of ground and Rydberg
states. A detailed analysis of relevant loss mechanisms shows that the overall
lifetime of such a system is limited only by the spontaneous decay of the
Rydberg state, and is not significantly affected by photoionization or
autoionization. The van der Waals C_6 coefficients for the 5sns series are
calculated, and we find that the interactions are attractive. Finally we show
that the combination of magic-wavelength lattices and attractive interactions
could be exploited to generate many-body Greenberger-Horne-Zeilinger (GHZ)
states.
