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

JOURNAL OF GEOMETRY AND PHYSICS

卷:84

Article

Dinar, Yassir Ibrahim^1,2 

[1] Sultan Qaboos Univ, Fac Sci, Dept Math & Stat, Muscat, Oman

[2] Abdus Salam Int Ctr Theoret Phys ICTP, Trieste, Italy

关键词: W-algebras;    Bihamiltonian reduction;    Drinfeld-Sokolov reduction;    Dirac reduction;    Slodowy slice;    Transverse Poisson structure;   

DOI  :  10.1016/j.geomphys.2014.06.003

来源: Elsevier

【 摘 要 】

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. (C) 2014 Elsevier B.V. All rights reserved.

【 授权许可】

Free