Hamiltonian reduction and classical extended superconformal algebras

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 Aγ from the hamiltonian reduction of the exceptional Lie superalgebra D(2vertical stroke1; γ/(1-γ)). We also find the Miura transformation for these algebras and give the free field representation. A W-algebraic generalization is discussed. (orig.)