caa a22 4500 467911525 CHVBK 20180406152850.0 cr unu---uuuuu 170328e20060601xx s 000 0 eng 10.1007/s11232-006-0078-5 doi (NATIONALLICENCE)springer-10.1007/s11232-006-0078-5 Shchepochkina I. Independent University of Moscow, Moscow, Russia aut How to realize a Lie algebra by vector fields [Elektronische Daten] [I. Shchepochkina] 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. Springer Science+Business Media, Inc., 2006 Cartan prolongation nationallicence nonintegrable distributions nationallicence $$\mathfrak{g}$$(2) structure nationallicence Theoretical and Mathematical Physics Kluwer Academic Publishers-Consultants Bureau 147/3(2006-06-01), 821-838 0040-5779 147:3<821 2006 147 11232 https://doi.org/10.1007/s11232-006-0078-5 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11232-006-0078-5 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Shchepochkina I. Independent University of Moscow, Moscow, Russia aut NATIONALLICENCE 773 0- Theoretical and Mathematical Physics Kluwer Academic Publishers-Consultants Bureau 147/3(2006-06-01), 821-838 0040-5779 147:3<821 2006 147 11232 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer