Communications in Mathematical Physics

, Volume 316, Issue 1, pp 269–277

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


DOI: 10.1007/s00220-012-1543-7

Cite this article as:
Dong, C. & Yu, N. Commun. Math. Phys. (2012) 316: 269. doi:10.1007/s00220-012-1543-7


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.

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of CaliforniaSanta CruzUSA

Personalised recommendations