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Computations in finite-dimensional Lie algebras
Discrete mathematics & theoretical computer science, Tome 1 (1997).

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This paper describes progress made in context with the construction of a general library of Lie algebra algorithms, called ELIAS (Eindhoven Lie Algebra System), within the computer algebra package GAP. A first sketch of the package can be found in Cohen and de Graaf[1]. Since then, in a collaborative effort with G. Ivanyos, the authors have continued to develop algorithms which were implemented in ELIAS by the second author. These activities are part of a bigger project, called ACELA and financed by STW, the Dutch Technology Foundation, which aims at an interactive book on Lie algebras (cf. Cohen and Meertens [2]). This paper gives a global description of the main ways in which to present Lie algebras on a computer. We focus on the transition from a Lie algebra abstractly given by an array of structure constants to a Lie algebra presented as a subalgebra of the Lie algebra of n×n matrices. We describe an algorithm typical of the structure analysis of a finite-dimensional Lie algebra: finding a Levi subalgebra of a Lie algebra. 
@article{DMTCS_1997_1_a11,
     author = {Cohen, A. M. and Graaf, W. A. and R\'onyai, L.},
     title = {Computations in finite-dimensional {Lie} algebras},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {1},
     year = {1997},
     doi = {10.46298/dmtcs.242},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.242/}
}
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Cohen, A. M.; Graaf, W. A.; Rónyai, L. Computations in finite-dimensional Lie algebras. Discrete mathematics & theoretical computer science, Tome 1 (1997). doi : 10.46298/dmtcs.242. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.242/

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