Lie pseudogroup

Summary

A Lie pseudogroup is a pseudogroup of local diffeomorphisms of a manifold that is cut out by a system of partial differential equations. Membership of a local diffeomorphism is decided by its jets up to a fixed order at each point. Isometries, conformal maps, symplectomorphisms, holomorphic maps and volume-preserving maps all form Lie pseudogroups. Lie pseudogroups were introduced by Lie and studied by Cartan as the infinite-dimensional analogues of Lie groups.