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Journal Articles Discrete Mathematics and Theoretical Computer Science Year : 1997

Computations in finite-dimensional Lie algebras


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.
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hal-00955695 , version 1 (05-03-2014)



A. M. Cohen, W. A. De Graaf, L. Rónyai. Computations in finite-dimensional Lie algebras. Discrete Mathematics and Theoretical Computer Science, 1997, Vol. 1, pp.129-138. ⟨10.46298/dmtcs.242⟩. ⟨hal-00955695⟩


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