Extensions and contractions of the Lie algebra of q-pseudodifferential symbols

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dc.creatorKhesin, Boris
dc.creatorLyubashenko, Volodymyr
dc.creatorRoger, Claude
dc.date1994-03-31
dc.date2008-02-20
dc.date.accessioned2026-07-07T09:21:48Z
dc.date.available2026-07-07T09:21:48Z
dc.descriptionWe construct cocycles on the Lie algebra of pseudo- and q-pseudodifferential symbols of one variable and on their close relatives: the sine-algebra and the Poisson algebra on two-torus. A ``quantum'' Godbillon-Vey cocycle on (pseudo)-differential operators appears in this construction as a natural generalization of the Gelfand-Fuchs 3-cocycle on periodic vector fields. We describe a nontrivial embedding of the Virasoro algebra into (a completion of) q-pseudodifferential symbols, and propose q-analogs of the KP and KdV-hierarchies admitting an infinite number of conserved charges.
dc.description39 pages, close to published version
dc.identifierhttps://arxiv.org/abs/hep-th/9403189
dc.identifierhttp://arxiv.org/abs/hep-th/9403189
dc.identifierJ. Funct. Anal. 143 (1997), no. 1, 55-97
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/155153
dc.subjectHigh Energy Physics - Theory
dc.subjectQuantum Algebra
dc.titleExtensions and contractions of the Lie algebra of q-pseudodifferential symbols
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