Lie-Poisson groups and the Miura transformation

Abstract

We point out that the recent proof of the Kupershmidt-Wilson theorem by Cheng and Mas-Ramos is underpinned by the Lie-Poisson property of the second Gel'fand-Dickey bracket. The supersymmetric Kupershmidt-Wilson theorem is also proved along these same lines. Finally we comment on the possible repercussions in the problem of the coproduct for W-algebras.

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Cited by in corpus (3)

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• Screening operators and Parabolic inductions for Affine W-algebras (with an appendix by Shigenori Nakatsuka)
• On the Miura and Backlund transformations associated with the supersymmetric Gelfand-Dickey bracket