Geodesic
An algorithm for analysis of the structure of finitely presented Lie algebras
Discrete mathematics & theoretical computer science, Tome 1 (1997).

Voir la notice de l'article provenant de la source Episciences

We consider the following problem: what is the most general Lie algebra satisfying a given set of Lie polynomial equations? The presentation of Lie algebras by a finite set of generators and defining relations is one of the most general mathematical and algorithmic schemes of their analysis. That problem is of great practical importance, covering applications ranging from mathematical physics to combinatorial algebra. Some particular applications are constructionof prolongation algebras in the Wahlquist-Estabrook method for integrability analysis of nonlinear partial differential equations and investigation of Lie algebras arising in different physical models. The finite presentations also indicate a way to q-quantize Lie algebras. To solve this problem, one should perform a large volume of algebraic transformations which is sharply increased with growth of the number of generators and relations. For this reason, in practice one needs to use a computer algebra tool. We describe here an algorithm for constructing the basis of a finitely presented Lie algebra and its commutator table, and its implementation in the C language. Some computer results illustrating our algorithmand its actual implementation are also presented. 
@article{DMTCS_1997_1_a12,
     author = {Gerdt, Vladimir P. and Kornyak, Vladimir V.},
     title = {An algorithm for analysis of the structure of finitely presented {Lie} algebras},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {1},
     year = {1997},
     doi = {10.46298/dmtcs.243},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.243/}
}
TY  - JOUR
AU  - Gerdt, Vladimir P.
AU  - Kornyak, Vladimir V.
TI  - An algorithm for analysis of the structure of finitely presented Lie algebras
JO  - Discrete mathematics & theoretical computer science
PY  - 1997
VL  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.243/
DO  - 10.46298/dmtcs.243
LA  - en
ID  - DMTCS_1997_1_a12
ER  - 
%0 Journal Article
%A Gerdt, Vladimir P.
%A Kornyak, Vladimir V.
%T An algorithm for analysis of the structure of finitely presented Lie algebras
%J Discrete mathematics & theoretical computer science
%D 1997
%V 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.243/
%R 10.46298/dmtcs.243
%G en
%F DMTCS_1997_1_a12
Gerdt, Vladimir P.; Kornyak, Vladimir V. An algorithm for analysis of the structure of finitely presented Lie algebras. Discrete mathematics & theoretical computer science, Tome 1 (1997). doi : 10.46298/dmtcs.243. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.243/

Cité par Sources :