The algebra of {ital q}-pseudodifferential symbols and the {ital q}-{ital W}{sub KP}{sup ({ital n})} algebra

Journal Article · Sun Dec 01 04:00:00 EST 1996 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.531745· OSTI ID:397475

Mas, J; Seco, M ^[1]

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1. Departamento de Fisica de Particulas Elementales, Universidad de Santiago, Santiago de Compostela, 15706 (Spain)

In this paper we continue with the program to explore the topography of the space of {ital W}-type algebras. In the present case, the starting point is the work of Khesin, Lyubashenko, and Roger on the algebra of {ital 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 {ital q}-deformations of {bold W}{sub KP} and related {bold 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. {copyright} {ital 1996 American Institute of Physics.}

• OSTI ID: 397475
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 12 Vol. 37; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

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