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Let $\mathfrak{g}$ be a finite-dimensional real or complex Lie algebra, andlet $\mu \in \mathfrak{g}^{*}$. In the first part of the paper, the relation isdiscussed between the derived algebra of the stabilizer of $\mu$ and the set ofcoadjoint orbits which have the same dimension as the orbit of $\mu$. In thesecond part, semisimple Lie algebras are considered, and the relation isdiscussed between the derived algebra of a centralizer and sheets.

The derived algebra of a stabilizer, families of coadjoint orbits, and sheets