[[Lie algebra homomorphism]]
# Kernel of a Lie algebra homomorphism

The **kernel** $\ker f$ of a [[Lie algebra homomorphism]] $f : \mathfrak{ g} \to \mathfrak{h}$ over a field $\mathbb{K}$ is a special case of the [[kernel of an algebra homomorphism]], #m/def/lie
i.e. $\ker f = f^{-1} \{ 0 \}$.
It follows from the general case that the kernel is necessarily a [[Lie algebra ideal]] of $\mathfrak{ g}$.

#
---
#state/tidy | #lang/en | #SemBr