Abstract
We give a comprehensive treatment of the super-W ∞(λ) algebra, an extension of the super-Virasoro algebra that contains generators of spin s ⩾ 1 2 . The parameter λ defines the embedding of the Virasoro subalgebra. We describe how to obtain the super-W ∞(λ) algebra from the associative algebra of superspace differential operators. We discuss the structure of this associative algebra and its relation with the so-called wedge algebra, in which the generators for given spin are restricted to finite-dimensional representations of sl(2). From the super-W ∞(λ) algebra one can obtain a variety of W ∞ algebras by consistent truncations for specific values of λ. Without truncation the algebras are formally isomorphic for different values of λ. We present a realization in terms of the currents of a supersymmetric bc system.
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