Tensor products of modules for a vertex operator algebra and vertex tensor categories. (English) Zbl 0848.17031

Brylinski, Jean-Luc (ed.) et al., Lie theory and geometry: in honor of Bertram Kostant on the occasion of his 65th birthday. Invited papers, some originated at a symposium held at MIT, Cambridge, MA, USA in May 1993. Boston, MA: Birkhäuser. Prog. Math. 123, 349-383 (1994).
This is an announcement of the authors’ series of works on a tensor theory of vertex operator algebras. The phenomena of such a tensor appeared in G. Moore and N. Seiberg’s work [Commun. Math. Phys. 123, 177-254 (1989; Zbl 0694.53074)]. The phenomena had also been used by D. Kazhdan and G. Lusztig in establishing a tensor theory of modules of affine Lie algebras with the same level and their categorical relations with quantum groups [Int. Math. Res. Not. 2, 21-29 (1991; Zbl 0726.17015)]. Moreover, the authors propose the concept of a vertex tensor (monomial) category of central charge \(c\), which is a special abelian category. Furthermore, they define a \(P(z)\)-tensor in terms of an intertwining map \(P(z)\) and give two constructions of such a tensor.
For the entire collection see [Zbl 0807.00014].


17B69 Vertex operators; vertex operator algebras and related structures
18E99 Categorical algebra
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