Completely integrable Hamiltonian systems and deformations of Lie algebras (Q1896478)

In the Adler-Kostant-Symes theorem, as applied to completely integrable systems, two Lie algebras \(G\) and \(G_0\) appear, with the same underlying vector space. This paper states that in the cases that \(G\) is a finite-dimensional, semi-simple Lie algebra, or \(G= {\mathfrak {sl}}_2 (\mathbb{C}) \otimes \mathbb{C} [t,t^{-1} ]\), there exists a Lie algebra which is a deformation (of order 1) of \(G_0\), and which itself deforms to \(G\). The proof (not fully included) is along cohomological reasonings.