C_1-cofiniteness and Fusion Products of Vertex Operator Algebras

Abstract

Let V be a vertex operator algebra. We prove that if U and W are C_1-cofinite {\mathbb N}-gradable V-modules, then a fusion product U\boxtimes W is well-defined and also a C_1-cofinite {\mathbb N}-gradable V-module, where the fusion product is defined by (logarithmic) intertwining operators. This is also true for C_2-cofinite {\mathbb N}-gradable modules.

This is a proceeding of "Conformal field theories and tensor categories" held in 2011, (editor Y.-Z Huang), Springer Proceedings in Mathematics & Statistics (2013)

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