https://diffgeom.subwiki.org/w/index.php?action=history&feed=atom&title=Lie_algebra_of_global_derivationsLie algebra of global derivations - Revision history2026-07-02T00:56:29ZRevision history for this page on the wikiMediaWiki 1.41.2https://diffgeom.subwiki.org/w/index.php?title=Lie_algebra_of_global_derivations&diff=824&oldid=prevVipul: 1 revision2008-05-18T19:48:14Z<p>1 revision</p>
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</td></tr></table>Vipulhttps://diffgeom.subwiki.org/w/index.php?title=Lie_algebra_of_global_derivations&diff=823&oldid=prevVipul: New page: {{sheaf analog|sheaf of derivations}} ==Definition== The '''Lie algebra of global derivations''' of a differential manifold is defined as follows: * As a set, it is the set of all [...2008-04-05T21:03:08Z<p>New page: {{sheaf analog|sheaf of derivations}} ==Definition== The '''Lie algebra of global derivations''' of a <a href="/wiki/Differential_manifold" title="Differential manifold">differential manifold</a> is defined as follows: * As a set, it is the set of all [...</p>
<p><b>New page</b></p><div>{{sheaf analog|sheaf of derivations}}<br />
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==Definition==<br />
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The '''Lie algebra of global derivations''' of a [[differential manifold]] is defined as follows:<br />
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* As a set, it is the set of all [[vector field]]s, or derivations, defined on the whole manifold<br />
* It has the structure of a <math>\R</math>-vector space under pointwise addition and scalar multiplication; more generally, it is a module over <math>C^\infty(M)</math>, the [[algebra of infinitely differentiable functions]], under left multiplication<br />
* It is a Lie algebra: the Lie bracket of two derivations <math>D_1</math> and <math>D_2</math> is given as:<br />
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<math>D_1 \circ D_2 - D_2 \circ D_1</math></div>Vipul