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arXiv · hep-th/9307190

The vacuum preserving Lie algebra of a classical W-algebra

L. Feher·L. O'Raifeartaigh·I. Tsutsui
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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 $§$ 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 $§$.

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L. Feher, L. O'Raifeartaigh, I. Tsutsui. 1993-08-02. The vacuum preserving Lie algebra of a classical W-algebra. https://doi.org/10.1016/0370-2693(93)90325-c

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