and a general deformation theory for pseudogroups was developed by Kunihiko Kodaira and D. C. Spencer. In the 1960s homological algebra was applied to the basic PDE questions involved, of over-determination; this though revealed that the algebra of the theory is potentially very heavy. In the same decade the interest for theoretical physics of infinite-dimensional Lie theory appeared for the first time, in the shape of current algebra. Intuitively, a Lie pseudogroup should be a pseudogroup which "originates" from a system of PDEs. There are many similar but inequivalent notions in the literature; the "right" one depends on which application one has in mind. However, all these various approaches involve the (finite- or infinite-dimensional) jet bundles of , which are asked to be a Lie groupoid. In particular, a Lie pseudogroup is called of finite order if it can be "reconstructed" from the space of its -jets. References External links Lie groups Algebraic structures Differential geometry Differential topology