Geodesic
How to realize a Lie algebra by vector fields
Teoretičeskaâ i matematičeskaâ fizika, Tome 147 (2006) no. 3, pp. 450-469

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We describe an algorithm for embedding a finite-dimensional Lie algebra (superalgebra) into a Lie algebra (superalgebra) of vector fields that is suitable for a ground field of any characteristic and also a way to select the Cartan, complete, and partial prolongations of the Lie algebra of vector fields using differential equations. We illustrate the algorithm with the example of Cartan's interpretation of the exceptional simple Lie algebra $\mathfrak g(2)$ as the Lie algebra preserving a certain nonintegrable distribution and also several other examples.
Mots-clés : Cartan prolongation
Keywords: nonintegrable distributions, $\mathfrak g(2)$ structure. 
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     author = {I. M. Shchepochkina},
     title = {How to realize a {Lie} algebra by vector fields},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {450--469},
     publisher = {mathdoc},
     volume = {147},
     number = {3},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2006_147_3_a3/}
}
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I. M. Shchepochkina. How to realize a Lie algebra by vector fields. Teoretičeskaâ i matematičeskaâ fizika, Tome 147 (2006) no. 3, pp. 450-469. http://geodesic.mathdoc.fr/item/TMF_2006_147_3_a3/