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.
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.
Source: Wikipedia "Index of a Lie algebra" · CC BY-SA 4.0
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