Subclasses of Type Ia Supernovae as the origin of [\alpha/Fe] ratios in
  dwarf spheroidal galaxies
  Recent extensive observations of Type Ia Supernovae (SNe Ia) have revealed
the existence of a diversity of SNe Ia, including SNe Iax. We introduce two
possible channels in the single degenerate scenario: 1) double detonations in
sub-Chandrasekhar (Ch) mass CO white dwarfs (WDs), where a thin He envelope is
developed with relatively low accretion rates after He novae even at low
metallicities, and 2) carbon deflagrations in Ch-mass possibly hybrid C+O+Ne
WDs, where WD winds occur at [Fe/H] ~ -2.5 at high accretion rates. These
subclasses of SNe Ia are rarer than `normal' SNe Ia and do not affect the
chemical evolution in the solar neighborhood, but can be very important in
metal-poor systems with stochastic star formation. In dwarf spheroidal galaxies
in the Local Group, the decrease of [\alpha/Fe] ratios at [Fe/H] ~ -2 to -1.5
can be produced depending on the star formation history. SNe Iax give high
[Mn/Fe], while sub-Ch-mass SNe Ia give low [Mn/Fe], and thus a model including
a mix of the two is favoured by the available observations.
