On the moment map for the variety of Lie algebras
| dc.creator | Lauret, Jorge | |
| dc.date | 2002-06-05 | |
| dc.date.accessioned | 2026-07-07T04:48:55Z | |
| dc.date.available | 2026-07-07T04:48:55Z | |
| dc.description | 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. | |
| dc.description | 26 pages | |
| dc.identifier | https://arxiv.org/abs/math/0206046 | |
| dc.identifier | http://arxiv.org/abs/math/0206046 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/64231 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Rings and Algebras | |
| dc.subject | Representation Theory | |
| dc.title | On the moment map for the variety of Lie algebras | |
| dc.type | text |