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Lie derivatives of order $$n$$ on the line. Tensor meaning of the Gelfand- Dikij bracket. (English) Zbl 0753.58008
Topics in representation theory, Adv. Sov. Math. 2, 221-231 (1991).
[For the entire collection see Zbl 0722.00010.]
The authors study invariant operations over geometric quantities. The Lie derivative of order 1 is defined by the Schouten bracket. The Lie derivative of order 2 is associated with the projective connection on the line. Using the differential Newton binomial of order $$n$$ the authors define in §3 the Lie derivative of order $$n$$. Finally §4 contains the interpretation of the suggested generalization of the Lie derivative.

##### MSC:
 37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems 17B65 Infinite-dimensional Lie (super)algebras 58A99 General theory of differentiable manifolds