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Communications in Mathematical Physics

, Volume 137, Issue 1, pp 109–132 | Cite as

Indecomposable modules over the Virasoro Lie algebra and a conjecture of V. Kac

  • Christiane Martin
  • Alain Piard
Article

Abstract

We consider a class of indecomposable modules over the Virasoro Lie algebra that we call bounded admissible modules. We get results concerning the center and the dimensions of the weight spaces. We prove that these modules always contain a submodule with one-dimensional weight spaces. From this follows the proof of a conjecture of V. Kac concerning the classification of simple admissible modules.

Keywords

Neural Network Statistical Physic Complex System Nonlinear Dynamics Quantum Computing 
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Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Christiane Martin
    • 1
  • Alain Piard
    • 1
  1. 1.Physique-MathématiqueUniversité de BourgogneDijon CedexFrance

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