Abstract
The tangent space to a jet manifold at a point has a module structure; this fact allows us to endow the Cartan subspace with a canonical bracket, a point-wise definition of its curvature. This bracket is related with the Spencer differential and an algebraic proof of the criterion on formal integrability given by Kruglikov and Lychagin is outlined.
On the other hand, we define the characteristic vectors of a system of partial differential equations in the framework of differential correspondences and show how the canonical bracket defined above can be used to compute them.
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Alonso, R.J., Jimènez, S., Rodríguez, J. (2009). Some Canonical Structures of Cartan Planes in Jet Spaces and Applications. In: Kruglikov, B., Lychagin, V., Straume, E. (eds) Differential Equations - Geometry, Symmetries and Integrability. Abel Symposia, vol 5. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00873-3_1
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