Hamiltonian Reduction and Classical Extended Superconformal Algebras

Abstract

We present a systematic construction of classical extended superconformal algebras from the hamiltonian reduction of a class of affine Lie superalgebras, which include an even subalgebra $sl(2)$. In particular, we obtain the doubly extended $N=4$ superconformal algebra ${\tilde{A}}_{\gamma }$ from the hamiltonian reduction of the exceptional Lie superalgebra $D(2|1;\gamma /(1-\gamma ))$. We also find the Miura transformation for these algebras and give the free field representation. A $W$-algebraic generalization is discussed.

13 pages

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