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

Huang, Yi-Zhi; Lepowsky, James

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].

Reviewer: Xu Xiaoping (Kowloon)

MSC:

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

Keywords:

Jacobi identity; intertwining operators; \(P(z)\)-tensor; tensor theory; vertex operator algebras

Citations:

Zbl 0694.53074; Zbl 0726.17015