Moving frames and prolongation algebras

摘要: We consider differential ideals generated by sets of 2‐forms which can be written with constant coefficients in a canonical basis 1‐forms. By setting up Cartan–Ehresmann connection, fiber bundle over base space the live, one finds an incomplete Lie algebra vector fields fibers. Conversely, given this (a prolongation algebra), derive ideal. The two constructs are thus dual, and analysis either derives properties both. Such systems arise classical geometry moving frames. Examples discussed, together examples arising more recently: Korteweg–de Vries Harrison–Ernst systems.