Physics – High Energy Physics – High Energy Physics - Theory

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1992-07-28

Commun.Math.Phys. 158 (1993) 17-44

Physics

High Energy Physics

High Energy Physics - Theory

31 pages, compressed uuencoded .dvi file, BONN-HE-92/20, US-FT-7/92, KUL-TF-92/20. [version just replaced was truncated by som

Scientific paper

10.1007/BF02097230

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 $\W_{1+\infty}$, $\W_\infty$ 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 $\widehat{\W}_\infty$ which contracts to a new nonlinear algebra of the $\W_\infty$-type.

**Figueroa-O'Farrill Jose M.**

Physics – High Energy Physics – High Energy Physics - Theory

Scientist

**Mas Javier**

Physics – High Energy Physics – High Energy Physics - Theory

Scientist

**Ramos Edgar**

Computer Science – Computational Geometry

Scientist

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