Generalizations of the Lax pair
1 Lax operator and the loop algebra
One can interpret ,
,
,
as generators of the
twisted loop superalgebra
.
The word ``twisted'' means that the power of the spectral parameter mod 4 should
correlate with the
-grading of the generators

where
replaces
etc.; operators
are generators of the
twisted loop superalgebra. Withe these new notations, the spectral parameter
is not present in
. Instead of entering explicitly in
, it now
parametrizes a representation of the generators
.






2 Further generalization
The basic relations (23) imply:
and similar equations for the commutators of
.

Eq. (36) we already discussed; it encodes the SUGRA constraints and at the same time defines
.
Eq. (37) is a theorem-definition: the theorem says that the left hand side is proportional
to
, and the definition is of 



It turns out, that there is the following generalization of the Lax pair: