### Abstract

Let g be a finite-dimensional real or complex Lie algebra, and let μ 2 g. In the first part of the paper, we discuss the relation between the derived Lie algebra of the stabilizer of μ and the set of coadjoint orbits which have the same dimension as the orbit of μ. In the second part, we consider semisimple Lie algebras and discuss the relation between the derived algebra of a centralizer and sheets.

Original language | English (US) |
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Pages (from-to) | 705-714 |

Number of pages | 10 |

Journal | Journal of Lie Theory |

Volume | 24 |

Issue number | 3 |

State | Published - Mar 12 2014 |

Externally published | Yes |

### Keywords

- Derived algebra of a centralizer
- Lie algebras
- Sheets

### ASJC Scopus subject areas

- Algebra and Number Theory

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## Cite this

Izosimov, A. (2014). The derived algebra of a stabilizer, families of coadjoint orbits, and sheets.

*Journal of Lie Theory*,*24*(3), 705-714.