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General properties of classical W algebras

F. Delduc·L. Frappat·E. Ragoucy·P. Sorba
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Abstract

After some definitions, we review in the first part of this talk the construction and classification of classical $W$ (super)algebras symmetries of Toda theories. The second part deals with more recently obtained properties. At first, we show that chains of $W$ algebras can be obtained by imposing constraints on some $W$ generators: we call secondary reduction such a gauge procedure on $W$ algebras. Then we emphasize the role of the Kac-Moody part, when it exists, in a $W$ (super) algebra. Factorizing out this spin 1 subalgebra gives rise to a new $W$ structure which we interpret either as a rational finitely generated $W$ algebra, or as a polynomial non linear $W_\infty$ realization. (Plenary talk presented by P. SORBA at the $XXII^{th}$ International Conference on Differential Geometric Methods in Theoretical Physics. Ixtapa Mexico, September 1993.)

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F. Delduc, L. Frappat, E. Ragoucy, P. Sorba. 1993-12-06. General properties of classical W algebras. https://arxiv.org/abs/hep-th/9312041

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