On the Moment Map for the Variety of Lie Algebras
نویسنده
چکیده
We consider the moment map m : PVn 7→ iu(n) for the action of GL(n) on Vn = Λ(C) ⊗ C. The critical points of the functional Fn = ||m|| : PVn 7→ R are studied, in order to understand the stratification of Ln ⊂ PVn defined by the negative gradient flow of Fn, where Ln is the algebraic subset of all Lie algebras. We obtain a description of the critical points which lie in Ln in terms of those which are nilpotent, as well as the minima and maxima of Fn : Ln 7→ R. A characterization of the critical points modulo isomorphism, as the union of categorical quotients of suitable actions is considered, and some applications to the study of Ln are given.
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تاریخ انتشار 2003