Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Lie Theory 26 (2016), No. 1, 169--179Copyright Heldermann Verlag 2016 Representing Lie Algebras Using Approximations with Nilpotent Ideals Wolfgang Alexander Moens Fakultät für Mathematik, Universität Wien, Oskar-Morgenstern-Platz 1, 1090 Wien, Austria wolfgang.moens@univie.ac.at [Abstract-pdf] We prove a refinement of Ado's theorem: a $d$-dimensional nilpotent Lie algebra over an algebraically closed field of characteristic zero with an ideal of class $\varepsilon_1$ and codimension $\varepsilon_2$ admits a faithful representation of degree ${d + \varepsilon_1\choose\varepsilon_1} \cdot {d + \varepsilon_2\choose\varepsilon_2}$. We then apply the theory of almost-algebraic hulls to generalise this result to the representation of arbitrary finite-dimensional Lie algebras and of Lie algebras graded by an abelian, finitely-generated, torsion-free group. Keywords: Lie algebra, representation, universal enveloping algebra, almost-algebraic Lie algebra, grading. MSC: 17B35 [ Fulltext-pdf  (295  KB)] for subscribers only.