Projective dimension and commuting variety of a reductive Lie algebra
Résumé
The commuting variety of a reductive Lie algebra g is the underlying variety of a well defined subscheme of g × g. In this note, it is proved that this scheme is normal and Cohen-Macaulay. In particular, its ideal of definition is a prime ideal. As a matter of fact, this theorem results from a so called Property (P) for a simple Lie algebra. This property says that some cohomology complexes are exact.
Origine : Fichiers produits par l'(les) auteur(s)
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