• Kenji Iohara
  • Yoshiyuki Koga
Part of the Springer Monographs in Mathematics book series (SMM)


We introduce the Virasoro algebra Vir as the universal central extension of the Witt algebra. This Lie algebra is a ℤ-graded Lie algebra and it is appropriate to work within the framework of what we call Q-graded Lie algebras. Hence, we also present a categorical setup for representations of Q-graded Lie algebras and some of their properties such as local composition series, (co)homologies, and Berstein-Gelfand-Gelfand duality.


Central Extension Free Abelian Group Verma Module High Weight Vector High Weight Module 
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Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.Institut Camille JordanUniversité Claude Bernard Lyon 1Villeurbanne CedexFrance
  2. 2.Department of Applied Physics, Faculty of EngineeringUniversity of FukuiFukuiJapan

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