The algebra of q-pseudodifferential symbols and the q-W_{KP}^n algebra

Details The algebra of q-pseudodifferential symbols and the q-W_{KP}^n algebra The algebra of q-pseudodifferential symbols and the q-W_{KP}^n algebra

1995-12-22

arxiv.org/abs/q-alg/9512025v3

Mathematics

Quantum Algebra

28 pages. Section 5 revised. Misprints corrected. References added

Scientific paper

10.1063/1.531745

In this paper we continue with the program to explore the topography of the space of W-type algebras. In the present case, the starting point is the work of Khesin, Lyubashenko and Roger on the algebra of q-deformed pseudodifferential symbols and their associated integrable hierarchies. The analysis goes on by studying the associated hamiltonian structures for which compact expressions are found. The fundamental Poisson brackets yield q-deformations of W_{KP} and related W-type algebras which, in specific cases, coincide with the ones constructed by Frenkel and Reshetikhin. The construction underlies a continuous correspondence between the hamiltonian structures of the Toda lattice and the KP hierarchies.

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