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