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Journal of Lie Theory 24 (2014), No. 3, 705--714
Copyright Heldermann Verlag 2014

The Derived Algebra of a Stabilizer, Families of Coadjoint Orbits, and Sheets

Anton Izosimov
Department of Mechanics and Mathematics, Moscow State University, Leninskie gori 1, Moscow 119991, Russia

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.

Keywords: Lie algebras, sheets, derived algebra of a centralizer.

MSC: 17B20

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