Discrete Mathematics & Theoretical Computer Science, Vol 1 (1997)

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DMTCS vol 1 no 1 (1997), pp. 129-138

Discrete Mathematics & Theoretical Computer Science


Volume 1 n° 1 (1997), pp. 129-138

author:A.M. Cohen and W.A. de Graaf and L. Rónyai
title:Computations in finite-dimensional Lie algebras
keywords:Lie algebra algorithms, ELIAS
abstract: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 packagecan 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.
reference: A.M. Cohen and W.A. de Graaf and L. Rónyai (1997), Computations in finite-dimensional Lie algebras, Discrete Mathematics and Theoretical Computer Science 1, pp. 129-138
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