On a refinement of Ado's theorem
The author studies the minimal dimension \(\mu(g)\) of a faithful \(g\)-module for \(n\)-dimensional nilpotent Lie algebras \(g\) (the nilpotent case is of particular interest since the invariant can be difficult to compute in this case). A known upper bound for \(\mu(g)\) of \(n^n+1\) is significantly improved to \(\alpha 2^n/\sqrt n\), where \(\alpha\sim 2.76287\), and much sharper upper bounds are obtained for various special classes of nilpotent Lie algebras such as filiform algebras and those admitting affine structures.
scientific article; zbMATH DE number 1145391