Authors: A. M. Cohen ^{1}; W. A. Graaf ^{1}; L. Rónyai ^{2}
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A. M. Cohen;W. A. Graaf;L. Rónyai
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.
Computing Bi-Invariant Pseudo-Metrics on Lie Groups for Consistent Statistics
2 Documents citing this article
Source : OpenCitations
Luzgarev, A. Yu.; Stepanov, Alexei; Vavilov, N., 2010, Calculations In Exceptional Groups Over Rings, Journal Of Mathematical Sciences, 168, 3, pp. 334-348, 10.1007/s10958-010-9984-z.
Miolane, Nina; Pennec, Xavier, 2015, Computing Bi-Invariant Pseudo-Metrics On Lie Groups For Consistent Statistics, Entropy, 17, 4, pp. 1850-1881, 10.3390/e17041850.