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• W2044852899 abstract "We construct cocycles on the Lie algebra of pseudo- andq-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 the Virasoro algebra into (a completion of)q-pseudodifferential symbols is proposed. We describeq-analogs of the KP and KdV-hierarchies admitting an infinite number of conserved charges as well asq-deformed Gelfand–Dickey structures." @default.
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• W2044852899 date "1997-01-01" @default.
• W2044852899 modified "2023-10-15" @default.
• W2044852899 title "Extensions and Contractions of the Lie Algebra ofq-Pseudodifferential Symbols on the Circle" @default.
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• W2044852899 doi "https://doi.org/10.1006/jfan.1996.2896" @default.
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