EXTENSIONS AND CONTRACTIONS OF THE LIE ALGEBRA OF q-PSEUDODIFFERENTIAL SYMBOLS BORIS KHESIN, VOLODIMIR LYUBASHENKO, AND CLAUDE ROGER
نویسندگان
چکیده
We construct cocycles on the Lie algebra of pseudoand 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.
منابع مشابه
Extensions and Contractions of the Lie Algebra of q-Pseudodifferential Symbols on the Circle
We construct cocycles on the Lie algebra of pseudoand 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. A nontrivial embedding of th...
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