  We study the stellar populations of SNe Ia host galaxies using SDSS-II
spectroscopy. We focus on the relationships of SNe Ia properties with stellar
velocity dispersion and the stellar population parameters age, metallicity and
element abundance ratios derived by fitting absorption line indices to stellar
population models. We concentrate on a sub-sample of 84 SNe Ia from the SDSS-II
Supernova Survey. In agreement with previous findings, we find that SALT2
stretch factor values show the strongest dependence on stellar population age.
Hence, SNe Ia peak-luminosity is closely related to the age of the stellar
progenitor systems, where more luminous SNe Ia appear in younger stellar
populations. We find no statistically significant trends in the Hubble residual
with any of the stellar population parameters studied, including age and
metallicity contrary to the literature, as well as with stellar velocity
dispersion. Moreover, we find that the method of stellar mass derivation is
affecting the Hubble residual-mass relationship when lower number statistics
are used. We extend the sample to also include SNe Ia with available SDSS host
galaxy photometry only. For this larger sample (247 objects) the reported
Hubble residual-mass relation is strongly dependent on the stellar mass range
studied and behaves as a step function. In the high mass regime, probed by our
host spectroscopy sample, the relation between Hubble residual and stellar mass
is flat. Below a stellar mass of ~2x10^10 Msun, i.e. close to the evolutionary
transition mass of low-redshift galaxies reported in the literature, the trend
changes dramatically such that lower mass galaxies possess lower luminosity SNe
Ia after light-curve corrections. This non-linear behaviour of the Hubble
residual-mass relationship should be accounted for when using stellar mass as a
further parameter for minimising the Hubble residuals.
