Minimal faithful representations of reductive Lie algebras

Abstract

We prove an explicit formula for the invariant $μ(\Lg)$ for finite-dimensional semisimple, and reductive Lie algebras $\Lg$ over $\C$. Here $μ(\Lg)$ is the minimal dimension of a faithful linear representation of $\Lg$. The result can be used to study Dynkin's classification of maximal reductive subalgebras of semisimple Lie algebras.

References in corpus (1)

• Abelian ideals in a Borel subalgebra of a complex simple Lie algebra