Extensions and contractions of the Lie algebra of q-pseudodifferential symbols
Abstract
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.
- Publication:
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arXiv e-prints
- Pub Date:
- March 1994
- DOI:
- 10.48550/arXiv.hep-th/9403189
- arXiv:
- arXiv:hep-th/9403189
- Bibcode:
- 1994hep.th....3189K
- Keywords:
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- High Energy Physics - Theory;
- Mathematics - Quantum Algebra
- E-Print:
- 39 pages, close to published version