Index of a Lie algebra

In algebra, let g be a Lie algebra over a field K. Let further ${\displaystyle \xi \in {\mathfrak {g}}^{*}}$ be a one-form on g. The stabilizer g_ξ of ξ is the Lie subalgebra of elements of g that annihilate ξ in the coadjoint representation. The index of the Lie algebra is

${\displaystyle \operatorname {ind} {\mathfrak {g}}:=\min \limits _{\xi \in {\mathfrak {g}}^{*}}\dim {\mathfrak {g}}_{\xi }.}$