Communications in Mathematical Physics

, Volume 316, Issue 1, pp 269–277

\({\mathbb{Z}}\) -Graded Weak Modules and Regularity



It is proved that if any \({\mathbb{Z}}\) -graded weak module for vertex operator algebra V is completely reducible, then V is rational and C2-cofinite. That is, V is regular. This gives a natural characterization of regular vertex operator algebras.


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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of CaliforniaSanta CruzUSA

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