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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