Journal of Lie Theory

no. 1
Representing Lie Algebras Using Approximations with Nilpotent Ideals
Journal of Lie Theory, Volume 26 (2016) no. 1, pp. 169-179
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.
DOI: 10.5802/jolt.885
Classification: 17B35
Keywords: Lie algebra, representation, universal enveloping algebra, almost-algebraic Lie algebra, grading 
@article{JOLT_2016_26_1_a7,
     author = {W. A. Moens},
     title = {Representing {Lie} {Algebras} {Using} {Approximations} with {Nilpotent} {Ideals}},
     journal = {Journal of Lie Theory},
     pages = {169--179},
     year = {2016},
     volume = {26},
     number = {1},
     doi = {10.5802/jolt.885},
     zbl = {1404.17023},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.885/}
}
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W. A. Moens. Representing Lie Algebras Using Approximations with Nilpotent Ideals. Journal of Lie Theory, Volume 26 (2016) no. 1, pp. 169-179. doi: 10.5802/jolt.885

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