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Decomposition varieties in semisimple Lie algebras

  Published:1998-10-01
 Printed: Oct 1998
  • Abraham Broer
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Abstract

The notion of decompositon class in a semisimple Lie algebra is a common generalization of nilpotent orbits and the set of regular semisimple elements. We prove that the closure of a decomposition class has many properties in common with nilpotent varieties, \eg, its normalization has rational singularities. The famous Grothendieck simultaneous resolution is related to the decomposition class of regular semisimple elements. We study the properties of the analogous commutative diagrams associated to an arbitrary decomposition class.
MSC Classifications: 14L30, 14M17, 15A30, 17B45 show english descriptions Group actions on varieties or schemes (quotients) [See also 13A50, 14L24, 14M17]
Homogeneous spaces and generalizations [See also 32M10, 53C30, 57T15]
Algebraic systems of matrices [See also 16S50, 20Gxx, 20Hxx]
Lie algebras of linear algebraic groups [See also 14Lxx and 20Gxx]
14L30 - Group actions on varieties or schemes (quotients) [See also 13A50, 14L24, 14M17]
14M17 - Homogeneous spaces and generalizations [See also 32M10, 53C30, 57T15]
15A30 - Algebraic systems of matrices [See also 16S50, 20Gxx, 20Hxx]
17B45 - Lie algebras of linear algebraic groups [See also 14Lxx and 20Gxx]
 

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