Lie Derivative
Frederic P. Miller, Agnes F. Vandome, John McBrewster
In mathematics, the Lie derivative, named after Sophus Lie by W?adys?aw ?lebodzi?ski, evaluates the change of one vector field along the flow of another vector field. The Lie derivative is a derivation on the algebra of tensor fields over a manifold M. The vector space of all Lie derivatives on M forms an infinite-dimensional Lie algebra with respect to the Lie bracket defined by [A,B] = mathcal{L}_A B = -mathcal{L}_B A. The Lie derivatives are represented by vector fields, as infinitesimal generators of flows (active diffeomorphisms) on M. Looking at it the other way around, the diffeomorphism group of M has the associated Lie algebra structure, of Lie derivatives, in a way directly analogous to the Lie group theory. Данное...
ISBN: 978-6-1306-2964-9
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Дата выхода: июль 2011