A new class of counterexamples to the integrability problem.
For many years, it was believed that the solvability of the integrability problem for a transitive Lie pseudogroup depends only on the local solvability of linear differential operators arising from the abelian quotients in Guillemin's Jordan-Hölder decomposition for the transitive Lie algebra associated to the pseudogroup. We provide an example of a transitive pseudogroup for which the integrability problem is not solvable and whose corresponding Jordan-Hölder sequence has only non-abelian quotients.
Conn
J F
JF
Department of Mathematics, Princeton University, Princeton, New Jersey 08540.