Abstract
We show how methods from cyclic homology give easily an explicit 2-cocycle ϕ on the Lie algebra of differential operators of the circle such that ϕ restricts to the cocycle defining the Virasoro algebra. The same methods yield also aq-analogue of ϕ as well as an infinite family of linearly independent cocycles arising when the complex parameterq is a root of unity. We use an algebra ofq-difference operators andq-analogues of Koszul and the Rham complexes to construct these “quantum” cocycles.
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Communicated by J. Fröhlich
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Kassel, C. Cyclic homology of differential operators, the Virasoro algebra and aq-analogue. Commun.Math. Phys. 146, 343–356 (1992). https://doi.org/10.1007/BF02102632
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DOI: https://doi.org/10.1007/BF02102632