### Abstract

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.

Original language | English |
---|---|

Pages (from-to) | 30-42 |

Number of pages | 13 |

Journal | Journal of Geometry and Physics |

Volume | 84 |

DOIs | |

Publication status | Published - 2014 |

### Fingerprint

### Keywords

- Bihamiltonian reduction
- Dirac reduction
- Drinfeld-Sokolov reduction
- Slodowy slice
- Transverse poisson structure
- W-algebras

### ASJC Scopus subject areas

- Mathematical Physics
- Physics and Astronomy(all)
- Geometry and Topology

### Cite this

**W-algebras and the equivalence of bihamiltonian, Drinfeld-Sokolov and Dirac reductions.** / Dinar, Yassir Ibrahim.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - W-algebras and the equivalence of bihamiltonian, Drinfeld-Sokolov and Dirac reductions

AU - Dinar, Yassir Ibrahim

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

KW - Bihamiltonian reduction

KW - Dirac reduction

KW - Drinfeld-Sokolov reduction

KW - Slodowy slice

KW - Transverse poisson structure

KW - W-algebras

UR - http://www.scopus.com/inward/record.url?scp=84903614163&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84903614163&partnerID=8YFLogxK

U2 - 10.1016/j.geomphys.2014.06.003

DO - 10.1016/j.geomphys.2014.06.003

M3 - Article

VL - 84

SP - 30

EP - 42

JO - Journal of Geometry and Physics

JF - Journal of Geometry and Physics

SN - 0393-0440

ER -