Abstract
It is proved that if any \({\mathbb{Z}}\) -graded weak module for vertex operator algebra V is completely reducible, then V is rational and C 2-cofinite. That is, V is regular. This gives a natural characterization of regular vertex operator algebras.
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Communicated by Y. Kawahigashi
Supported by NSF grants, and a Faculty research grant from the University of California at Santa Cruz.
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Dong, C., Yu, N. \({\mathbb{Z}}\) -Graded Weak Modules and Regularity. Commun. Math. Phys. 316, 269–277 (2012). https://doi.org/10.1007/s00220-012-1543-7
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DOI: https://doi.org/10.1007/s00220-012-1543-7