Nonmeromorphic operator product expansion and<i>C</i>₂-cofiniteness for a family of -algebras

Abstract

We prove the existence and associativity of the nonmeromorphic operator product expansion for an infinite family of vertex operator algebras, the triplet W-algebras, using results from P(z)-tensor product theory. While doing this, we also show that all these vertex operator algebras are C_2-cofinite.