General properties of classical W algebras
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∞ realization. (Plenary talk presented by P. SORBA at the XXIIth International Conference on Differential Geometric Methods in Theoretical Physics. Ixtapa Mexico, September 1993.)
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