The Classical Exchange Algebra of AdS5 x S^5

The classical exchange algebra satisfied by the monodromy matrix of AdS₅ x S⁵ string theory in the Green-Schwarz formulation is determined by using a first-order Hamiltonian formulation and by adding to the Bena-Polchinski-Roiban Lax connection terms proportional to constraints. This enables in particular to show that the conserved charges of this theory are in involution. This result is obtained for a general world-sheet metric. The same exchange algebra is obtained within the pure spinor description of AdS₅ x S⁵ string theory. These results are compared to the one obtained by A. Mikhailov and S. Schaefer-Nameki for the pure spinor formulation