Ovsienko, O. D.; Ovsienko, V. Yu. 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. Reviewer: P.Grushko (Irkutsk) Cited in 1 Document MSC: 37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems 17B65 Infinite-dimensional Lie (super)algebras 58A99 General theory of differentiable manifolds Keywords:Lie derivative of higher order; Gel’fand-Dikij bracket Citations:Zbl 0722.00010 PDFBibTeX XMLCite \textit{O. D. Ovsienko} and \textit{V. Yu. Ovsienko}, in: Representations of infinite-dimensional classical groups, limits of enveloping algebras, and Yangians. . 221--231 (1991; Zbl 0753.58008)