HIGHER-SPIN THEORIES, W-INFINITY ALGEBRAS AND THEIR SUPEREXTENSIONS
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We examine the role of higher-spin algebras in (2 + 1) and (1 + 1) dimensional. We construct (2 + 1)-dimensional Chern-Simons theories based on bosonic and supersymmetric extensions of the anti-de Sitter group, and show how the resulting higher-spin algebras are related to the algebra of symplectic diffeomorphisms of the plane and the super-plane. We also construct N=1 and N=2 supersymmetric extensions of the W algebra of conformal fields in (1 + 1) dimension, with all spins 3 2, and indicate how these are related to the symplectic diffeomorphisms mentioned above. 1990.
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