$W$-algebras and the equivalence of bihamiltonian, Drinfeld-Sokolov and Dirac reductions

Autor:	Dinar, Yassir
Rok vydání:	2009
Předmět:	Mathematics - Differential Geometry Mathematical Physics Mathematics - Representation Theory Mathematics - Symplectic Geometry 37K10 35D45
Druh dokumentu:	Working Paper
Popis:	We prove that the classical $W$-algebra associated to a nilpotent orbit in a simple Lie-algebra can be constructed by preforming bihamiltonian, Drinfeld-Sokolov or Dirac reductions. We conclude that the classical $W$-algebra depends only on the nilpotent orbit but not on the choice of a good grading or an isotropic subspace. In addition, using this result we prove again that the transverse Poisson structure to a nilpotent orbit is polynomial and we better clarify the relation between classical and finite $W$-algebras. Comment: revised for clarity
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/0911.2116 Zobrazit plný text záznamu View this record from Arxiv