A remark on homogeneous affine varieties and related matters.
Résumé
In this note we give an example of affine quotient $G/H$ where $G$ is an affine algebraic group over an algebraically closed field of characteristic $0$ and $H$ is a unipotent subgroup not contained in the unipotent radical of $G$. Some remarks about symmetric algebras of centralizers of nilpotent elements in simple Lie algebras, in particular cases, are added.
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