This article is cited in 33 papers

How to realize a Lie algebra by vector fields

I. M. Shchepochkina

Independent University of Moscow

Abstract: 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.

Keywords: Cartan prolongation, nonintegrable distributions, $\mathfrak g(2)$ structure.

Received: 21.09.2005
Revised: 08.12.2005

DOI: 10.4213/tmf1987

 English version: Theoretical and Mathematical Physics, 2006, 147:3, 821–838

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