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: