Journal of Lie Theory

no. 3
The Derived Algebra of a Stabilizer, Families of Coadjoint Orbits, and Sheets
Journal of Lie Theory, Volume 24 (2014) no. 3, pp. 705-714
Let g be a finite-dimensional real or complex Lie algebra, and let μ be an element of 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.
DOI: 10.5802/jolt.802
Classification: 17B20
Keywords: Lie algebras, sheets, derived algebra of a centralizer 
@article{JOLT_2014_24_3_a4,
     author = {A. Izosimov},
     title = {The {Derived} {Algebra} of a {Stabilizer,} {Families} of {Coadjoint} {Orbits,} and {Sheets}},
     journal = {Journal of Lie Theory},
     pages = {705--714},
     year = {2014},
     volume = {24},
     number = {3},
     doi = {10.5802/jolt.802},
     zbl = {1373.17015},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.802/}
}
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A. Izosimov. The Derived Algebra of a Stabilizer, Families of Coadjoint Orbits, and Sheets. Journal of Lie Theory, Volume 24 (2014) no. 3, pp. 705-714. doi: 10.5802/jolt.802

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