W(2)n algebras

We construct W-algebra generalizations of the sl(2) algebra-W algebras W-n((2)) generated by two currents epsilon and F with the highest pole of order n in their OPE. The n = 3 term in this series is (2) the Bershadsky-Polyakov W-3((2)) algebra. We define these algebras as a centralizer (commutant) of the U(q)sl(n\l) quantum supergroup and explicitly find the generators in a factored, Miura-like (2) form. Another construction of the W-n((2)) algebras is in terms of the coset sl(n\1)/sl(n). The relation between the two constructions involves the duality (k + n - 1)(k' + n - 1) = 1 between levels k and k' of two sl(n) algebras. (C) 2004 Published by Elsevier B.V.