Lie algebras and Korteweg-de Vries equations (Q1101903)

For each Lie algebra admitting a bi-invariant two-form, the author constructs an infinite commuting hierarchy of bi-Hamiltonian integrable extensions of the KdV family. The technique of the construction is based on the Lie-Poisson theory on the dual space of a carefully constructed one parameter family of differential Lie algebras. The paper is self- contained and, even the sometimes tedious technical proofs, are complete.