On the moment map for the variety of Lie algebras

Details On the moment map for the variety of Lie algebras On the moment map for the variety of Lie algebras

2002-06-05

arxiv.org/abs/math/0206046v1

Mathematics

Algebraic Geometry

26 pages

Scientific paper

Let V be the vector space of all skew-symmetric (non-associative) complex algebras of dimension n and L the algebraic subset of V of all Lie algebras. We consider the moment map for the action of GL(n) on the projective space P(V) and study the critical points of the functional F:square norm of the moment map, in order to understand the stratification of L defined by the negative gradient flow of F. We obtain a description of the critical points which lie in L in terms of those which are nilpotent, as well as the minima and maxima of F on L. A characterization of the critical points modulo isomorphism, as the finite union of categorical quotients of suitable actions is considered, and some applications to the study of L are given.

Affiliated with

Also associated with

No associations

Rating

On the moment map for the variety of Lie algebras does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the moment map for the variety of Lie algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the moment map for the variety of Lie algebras will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-574454