Virasoro Vertex Operator Algebras, the (Nonmeromorphic) Operator Product Expansion and the Tensor Product Theory

✍ Scribed by Yi-Zhi Huang

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 341 KB
• Volume: 182
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.1996.0168

✦ Synopsis

A theory of tensor products of modules for a vertex operator algebra is being developed by Lepowsky and the author. To use this theory, one first has to verify that the vertex operator algebra satisfies certain conditions. We show in the present paper that for any vertex operator algebra containing a vertex operator subalgebra isomorphic to a tensor product algebra of minimal Virasoro vertex Ž . operator algebras vertex operator algebras associated to minimal models , the tensor product theory can be applied. In particular, intertwining operators for such Ž . Ž . a vertex operator algebra satisfy the nonmeromorphic commutativity locality Ž . Ž . and the nonmeromorphic associativity operator product expansion . Combined with a result announced by Lepowsky and the author in 1994, the results of the present paper also show that the category of modules for such a vertex operator algebra has a natural structure of a braided tensor category. In particular, for any pair p, q of relatively prime positive integers larger than 1, the category of minimal wŽ . 2 x modules of central charge 1 y 6 p y q rpq for the Virasoro algebra has a natural structure of a braided tensor category.