  We present Monte Carlo simulation results on the equilibrium relaxation
dynamics in the two dimensional lattice Coulomb gas, where finite fraction $f$
of the lattice sites are occupied by positive charges. In the case of high
order rational values of $f$ close to the irrational number $1-g$
($g\equiv(\sqrt{5} -1)/2$ is the golden mean), we find that the system
exhibits, for wide range of temperatures above the first-order transition, a
glassy behavior resembling the primary relaxation of supercooled liquids.
Single particle diffusion and structural relaxation show that there exists a
breakdown of proportionality between the time scale of diffusion and that of
structural relaxation analogous to the violation of the Stokes-Einstein
relation in supercooled liquids. Suitably defined dynamic cooperativity is
calculated to exhibit the characteristic nature of dynamic heterogeneity
present in the system.
