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Teoreticheskaya i Matematicheskaya Fizika, 2006, Volume 147, Number 3, Pages 450–469
DOI: https://doi.org/10.4213/tmf1987 (Mi tmf1987) 		 
This article is cited in 31 scientific papers (total in 31 papers)

How to realize a Lie algebra by vector fields

I. M. Shchepochkina

Independent University of Moscow
Full-text PDF (555 kB) Citations (31)
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DOI: https://doi.org/10.4213/tmf1987
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
English version:
Theoretical and Mathematical Physics, 2006, Volume 147, Issue 3, Pages 821–838
DOI: https://doi.org/10.1007/s11232-006-0078-5
Bibliographic databases:
Language: Russian
Citation: I. M. Shchepochkina, “How to realize a Lie algebra by vector fields”, TMF, 147:3 (2006), 450–469; Theoret. and Math. Phys., 147:3 (2006), 821–838
Citation in format AMSBIB
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    • This publication is cited in the following 31 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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