The vacuum preserving Lie algebra of a classical W-algebra

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

1993-07-30

arxiv.org/abs/hep-th/9307190v2

Phys.Lett. B316 (1993) 275-281

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1016/0370-2693(93)90325-C

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 M\"obius $sl(2)$ 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 $\W_\S^\G$-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 M\"obius $sl(2)$ is identified with $\S$.

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