Lax pair for
Let us look at how it works for .
where . This is a tautology.
However, there is a nontrivial generalization, leading to the integrability:
However, there is a nontrivial generalization, leading to the integrability:
with . Notice that we obtained the nontrivial Lax pair from
the tautological one by replacing with some twisted loop algebra.
What can we say from our point of view? We seem to need:
what could this mean?
Idea: let us further extend this algebra to something like a sum of two SYM algebras.