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

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

1994-03-31

arxiv.org/abs/hep-th/9403189v4

J. Funct. Anal. 143 (1997), no. 1, 55-97

Physics

High Energy Physics

High Energy Physics - Theory

39 pages, close to published version

Scientific paper

We 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.

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