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

Bibcode
1994hep.th....3189K
Khesin, Boris; Lyubashenko, Volodymyr; Roger, Claude
Bibliographical reference

eprint arXiv:hep-th/9403189

Advertised on:
3
1994
Number of authors
3
IAC number of authors
0
Citations
7
Refereed citations
4
Description
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.
Type
Non-refereed

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