The vacuum preserving Lie algebra of a classical W-algebra

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 $\W_§^\G$-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 $\S$.

11 pages, BONN-HE-93-25, DIAS-STP-93-13. Some typos had been removed, no change in formulas

References in corpus (2)

• W-symmetry in Conformal Field Theory
• On the classification of quantum W-algebras

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