The algebra was essentially guessed. But it turns out that it has a natural interpretation in the string worldsheet theory.
For the pure spinor superstring in the Lax pair was constructed by B.C.Vallilo:
where are generators of :
and are currents:
and is a complex number which is called spectral parameter.
It follows from the equations of motion that . This observation can be taken as a starting point of the classical integrability theory.
We will now discuss generalizations of this construction.