Extensions and contractions of the Lie algebra of qpseudodifferential symbols
Abstract
We construct cocycles on the Lie algebra of pseudo and qpseudodifferential symbols of one variable and on their close relatives: the sinealgebra and the Poisson algebra on twotorus. A ``quantum'' GodbillonVey cocycle on (pseudo)differential operators appears in this construction as a natural generalization of the GelfandFuchs 3cocycle on periodic vector fields. We describe a nontrivial embedding of the Virasoro algebra into (a completion of) qpseudodifferential symbols, and propose qanalogs of the KP and KdVhierarchies admitting an infinite number of conserved charges.
 Publication:

arXiv eprints
 Pub Date:
 March 1994
 DOI:
 10.48550/arXiv.hepth/9403189
 arXiv:
 arXiv:hepth/9403189
 Bibcode:
 1994hep.th....3189K
 Keywords:

 High Energy Physics  Theory;
 Mathematics  Quantum Algebra
 EPrint:
 39 pages, close to published version