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.