Two abelian subalgebras 
The even subalgebra of
is a direct sum of two Lie algebras:
(The real form would be
and
.) Schematically,
in the
-block notations:
The
in the upper right corner and
in the lower left corner are both
odd abelian subalgebras isomorphic to
.
The 
grading which was used to construct the 
-model action
is not very transparent in these notations. Notice that:
and 
are contained in 
and 
is some linear combination of 
and 
and
is the linear combination with the opposite relative sign between
and
(The real form would be