A one-parameter family of hamiltonian structures for the KP hierarchy and a continuous deformation of the nonlinear WKP algebra

1992/07/31 by José Figueroa-O’Farrill, J. M. Figueroa-O'Farrill, Javier Mas +3 · 5 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #hep-th

paper · pdf · doi:10.1007/bf02097230

published as Commun.Math.Phys. 158 (1993) 17-44 · 31 pages, compressed uuencoded .dvi file, BONN-HE-92/20, US-FT-7/92, KUL-TF-92/20. [version just replaced was truncated by some mailer]

arxiv created 1993/03/25 · openalex publication_date 1993/11/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The KP hierarchy is hamiltonian relative to a one-parameter family of Poisson structures obtained from a generalized Adler map in the space of formal pseudodifferential symbols with noninteger powers. The resulting \W-algebra is a one-parameter deformation of \W_{\rm KP} admitting a central extension for generic values of the parameter, reducing naturally to \W_n for special values of the parameter, and contracting to the centrally extended \W_1+∞, \W_∞ and further truncations. In the classical limit, all algebras in the one-parameter family are equivalent and isomorphic to \w_{\rm KP}. The reduction induced by setting the spin-one field to zero yields a one-parameter deformation of \widehat\W_∞ which contracts to a new nonlinear algebra of the \W_∞-type.

Citations

• W-symmetry in Conformal Field Theory

Cited by

• On diff(S1) covariantization of pseudodifferential operator
• A new approach to deformation equations of noncommutative KP hierarchies
• On the Kadomtsev-Petviashvili hierarchy in an extended class of formal pseudo-differential operators
• Exploring W ∞ W_∞ in the quadratic basis
• A geometry for multidimensional integrable systems