### 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) |
---|---|

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 |

### Fingerprint

### Keywords

- Derived algebra of a centralizer
- Lie algebras
- Sheets

### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*Journal of Lie Theory*,

*24*(3), 705-714.

**The derived algebra of a stabilizer, families of coadjoint orbits, and sheets.** / Izosimov, Anton.

Research output: Contribution to journal › Article

*Journal of Lie Theory*, vol. 24, no. 3, pp. 705-714.

}

TY - JOUR

T1 - The derived algebra of a stabilizer, families of coadjoint orbits, and sheets

AU - Izosimov, Anton

PY - 2014/3/12

Y1 - 2014/3/12

N2 - 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.

AB - 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.

KW - Derived algebra of a centralizer

KW - Lie algebras

KW - Sheets

UR - http://www.scopus.com/inward/record.url?scp=84897723237&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84897723237&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84897723237

VL - 24

SP - 705

EP - 714

JO - Journal of Lie Theory

JF - Journal of Lie Theory

SN - 0949-5932

IS - 3

ER -