  The potential importance of the angular momentum which is gained by accreting
white dwarfs (WDs) has been increasingly recognized in the context of type Ia
supernova (SN Ia) single-degenerate model. The expectation that the spin of the
WD can delay the explosion should help the single-degenerate model to be
consistent with the observed properties of most SNe Ia, in particular by
avoiding hydrogen contamination. In this article, we attempt to study the most
prominent single-degenerate supersoft (WD + MS) channel when the rotation of
accreting WDs is considered. We present a detailed binary population synthesis
study to examine the predicted population of SNe Ia for this channel. For our
standard model, we find that 77% of these SNe Ia explode with WD masses which
are low enough to be supported by solid-body rotation (1.378-1.5Msun); this is
a substantially higher proportion than found by previous work. Only 2% have WD
explosion masses >2.0Msun; these require the initial WD mass to be larger than
1.0 Msun. We further discuss the possible origin of the diversity of SNe Ia
from the pre- and post- accretion properties of the WDs in this population. We
also suggest that some SN Ia progenitors with substantial circumstellar
hydrogen, including some apparent type IIn SNe, might be related to WDs which
required support from differential rotation to avoid explosion, since these can
still be accreting from hydrogen-rich donors with a relatively high
mass-transfer rate at the time of the SN explosion.
