Lie bracket of differential operators

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Revision as of 20:13, 5 April 2008 by Vipul (talk | contribs) (New page: ==Definition== Let <math>M</math> be a differential manifold and <math>D_1,D_2</math> be differential operators from <math>C^\infty(M)</math> to <math>C^\infty(M)</math>. The '''L...)
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Definition

Let M be a differential manifold and D_1,D_2 be differential operators from C^\infty(M) to C^\infty(M). The Lie bracket of D_1 and D_2 denoted [D_1,D_2] is defined as the following differential operator:

D_1 \circ D_2 - D_2 \circ D_1

Particular cases