  We take advantage of the exceptional photometric coverage provided by the
combination of GALEX data in the UV and the ALHAMBRA survey in the optical and
near-IR to analyze the physical properties of a sample of 1225 GALEX-selected
Lyman break galaxies (LBGs) at $0.8 \lesssim z \lesssim 1.2$ located in the
COSMOS field. This is the largest sample of LBGs studied at that redshift range
so far. According to a spectral energy distribution (SED) fitting with
synthetic stellar population templates, we find that LBGs at $z \sim 1$ are
mostly young galaxies with a median age of 341 Myr and have intermediate dust
attenuation, $\ < E_s (B-V) \ > \sim 0.20$. Due to their selection criterion,
LBGs at $z \sim 1$ are UV-bright galaxies and have high dust-corrected total
SFR, with a median value of 16.9 $M_\odot {\rm yr}^{-1}$. Their median stellar
mass is $\log{\left(M_*/M_\odot \right)} = 9.74$. We obtain that the
dust-corrected total SFR of LBGs increases with stellar mass and the specific
SFR is lower for more massive galaxies. Only 2% of the galaxies selected
through the Lyman break criterion have an AGN nature. LBGs at $z \sim 1$ are
mostly located over the blue cloud of the color-magnitude diagram of galaxies
at their redshift, with only the oldest and/or the dustiest deviating towards
the green valley and red sequence. Morphologically, 69% of LBGs are disk-like
galaxies, with the fraction of interacting, compact, or irregular systems being
much lower, below 12%. LBGs have a median effective radius of 2.5 kpc and
bigger galaxies have higher total SFR and stellar mass. Comparing to their
high-redshift analogues, we find evidence that LBGs at lower redshifts are
bigger, redder in the UV continuum, and have a major presence of older stellar
populations in their SEDs. However, we do not find significant difference in
the distributions of stellar mass or dust attenuation.
