A. M. Cohen ; W. A. Graaf ; L. Rónyai - Computations in finite-dimensional Lie algebras

dmtcs:242 - Discrete Mathematics & Theoretical Computer Science, January 1, 1997, Vol. 1 - https://doi.org/10.46298/dmtcs.242
Computations in finite-dimensional Lie algebrasArticle

Authors: A. M. Cohen 1; W. A. Graaf 1; L. Rónyai 2

  • 1 Department of mathematics and computing science [Eindhoven]
  • 2 Computer and Automation Research Institute [Budapest]

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.


Volume: Vol. 1
Published on: January 1, 1997
Imported on: March 26, 2015
Keywords: ELIAS,Lie algebra algorithms,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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