### Abstract

We simplify and generalize an argument due to Bowcock and Watts showing that one can associate a finite Lie algebra (the "classical vacuum preserving algebra") containing the Möbius sl(2) subalgebra to any classical W-algebra. Our construction is based on a kinematical analysis of the Poisson brackets of quasi-primary fields. In the case of the W^{G}_{S}-algebra constructed through the Drinfeld-Sokolov reduction based on an arbitrary sl(2) subalgebra S of a simple Lie algebra G, we exhibit a natural isomorphism between this finite Lie algebra and G whereby the Möbius sl(2) is identified with S.

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

Pages (from-to) | 275-281 |

Number of pages | 7 |

Journal | Physics Letters B |

Volume | 316 |

Issue number | 2-3 |

DOIs | |

Publication status | Published - Oct 21 1993 |

### Fingerprint

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Physics Letters B*,

*316*(2-3), 275-281. https://doi.org/10.1016/0370-2693(93)90325-C

**The vacuum preserving Lie algebra of a classical W-algebra.** / Fehér, L.; O'Raifeartaigh, L.; Tsutsui, I.

Research output: Contribution to journal › Article

*Physics Letters B*, vol. 316, no. 2-3, pp. 275-281. https://doi.org/10.1016/0370-2693(93)90325-C

}

TY - JOUR

T1 - The vacuum preserving Lie algebra of a classical W-algebra

AU - Fehér, L.

AU - O'Raifeartaigh, L.

AU - Tsutsui, I.

PY - 1993/10/21

Y1 - 1993/10/21

N2 - We simplify and generalize an argument due to Bowcock and Watts showing that one can associate a finite Lie algebra (the "classical vacuum preserving algebra") containing the Möbius sl(2) subalgebra to any classical W-algebra. Our construction is based on a kinematical analysis of the Poisson brackets of quasi-primary fields. In the case of the WGS-algebra constructed through the Drinfeld-Sokolov reduction based on an arbitrary sl(2) subalgebra S of a simple Lie algebra G, we exhibit a natural isomorphism between this finite Lie algebra and G whereby the Möbius sl(2) is identified with S.

AB - We simplify and generalize an argument due to Bowcock and Watts showing that one can associate a finite Lie algebra (the "classical vacuum preserving algebra") containing the Möbius sl(2) subalgebra to any classical W-algebra. Our construction is based on a kinematical analysis of the Poisson brackets of quasi-primary fields. In the case of the WGS-algebra constructed through the Drinfeld-Sokolov reduction based on an arbitrary sl(2) subalgebra S of a simple Lie algebra G, we exhibit a natural isomorphism between this finite Lie algebra and G whereby the Möbius sl(2) is identified with S.

UR - http://www.scopus.com/inward/record.url?scp=0009982063&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0009982063&partnerID=8YFLogxK

U2 - 10.1016/0370-2693(93)90325-C

DO - 10.1016/0370-2693(93)90325-C

M3 - Article

AN - SCOPUS:0009982063

VL - 316

SP - 275

EP - 281

JO - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

SN - 0370-2693

IS - 2-3

ER -