[[Lie algebra]]
# Central ideal

A **central ideal** $\mathfrak{a} \trianglelefteq \mathfrak{z} (\mathfrak{g}) \trianglelefteq \mathfrak{g}$ of a [[Lie algebra]] $\mathfrak{g}$ is a linear subspace of its [[Centre of a Lie algebra|centre]] $\Cent \mathfrak{g}$. #m/def/lie 
Any such subspace is necessarily an [[Lie algebra ideal|ideal]], since $[\mathfrak{a}, \mathfrak{g}] = \{ 0 \}$.
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#state/tidy | #lang/en | #SemBr