Generalized Drinfel'd-Sokolov hierarchies - Timothy Hollowood (Communications in Mathematical Physics, 1991)
In this paper we examine the bi-Hamiltonian structure of the generalized KdV-hierarchies. We verify that both Hamiltonian structures take the form of Kirillov brackets on the Kac-Moody algebra, and that they define a coordinated system. Classical extended conformal algebras are obtained from the second Poisson bracket. In particular, we construct the $W_n~l$ algebras, first discussed for the case $n=3$ and $l=2$ by A. Polyakov and M.