Lie algebraic computation In this paper the authors describe some basic algorithms for the structure determination of Lie algebras. They are implemented in a general library of Lie algebra algorithms, called ELIAS (for Eindhoven LIe Algebra System) which is built into the computer algebra package GAP. 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 [A. M. Cohen and L. Meertens, The ACELA project: Aims and Plans, to appear in: Human Interaction for Symbolic Computation, Texts and Monographs in Symbolic Computation, N. Kajler, (ed.) (Springer-Verlag, Vienna)]. Section 2 of this paper gives a global description of the main ways to present Lie algebras on a computer. Section 3 briefly discusses the intended functionality offered in the library as well as four specific algorithms.
Keywords for this software
References in zbMATH (referenced in 8 articles , 1 standard article )
Showing results 1 to 8 of 8.
- Luzgarev, A.; Stepanov, A.; Vavilov, N.: Calculations in exceptional groups over rings. (2010)
- De Loera, Jesús A.; McAllister, Tyrrell B.: On the computation of Clebsch-Gordan coefficients and the dilation effect (2006)
- de Graaf, W. A.: Using Cartan subalgebras to calculate nilradicals and Levi subalgebras of Lie algebras (1999)
- Cohen, A. M.; de Graaf, W. A.; Rónyai, L.: Computations in finite-dimensional Lie algebras (1997)
- Cohen, Arjeh M.; Ivanyos, Gábor; Wales, David B.: Finding the radical of an algebra of linear transformations (1997)
- de Graaf, W. A.: An algorithm for the decomposition of semisimple Lie algebras (1997)
- De Graaf, Willem A.: Algorithms for finite-dimensional Lie algebras (1997)
- Cohen, A. M.; de Graaf, W. A.: Lie algebraic computation (1996)