$P_{\infty }$ algebra of KP, free fermions and 2-cocycle in the Lie algebra of pseudodifferential operators

A. Yu. Orlov, P. Winternitz

The symmetry algebra $P_{\infty }=W_{\infty }\oplus H\oplus I_{\infty }$ of integrable systems is defined. As an example the classical Sophus Lie point symmetries of all higher KP equat…