Centralizer of an element of a Lie algebra
= Centralizer of an element of a Lie algebra
{title2=$Z_{\mathfrak g}(x)$}
= Lie algebra centralizer
{c}
{synonym}
For an element $x$ of a <Lie algebra> $\mathfrak g$, its centralizer is the <Lie subalgebra> $Z_{\mathfrak g}(x)=\{y\in\mathfrak g:[y,x]=0\}$, equivalently the <kernel> of $\operatorname{ad}x$ in the <Adjoint representation>.