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Communications in Mathematical Physics

, Volume 146, Issue 2, pp 343–356 | Cite as

Cyclic homology of differential operators, the Virasoro algebra and aq-analogue

  • Christian Kassel
Article

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.

Keywords

Neural Network Statistical Physic Complex System Nonlinear Dynamics Differential Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Christian Kassel
    • 1
  1. 1.Institut de Recherche Mathématique AvancéeUniversité Louis Pasteur-C.N.R.S.StrasbourgFrance

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