Selecta Mathematica

, 6:225

Generalized rationality and a ''Jacobi identity'' for intertwining operator algebras

  • Y.-Z. Huang

DOI: 10.1007/PL00001389

Cite this article as:
Huang, YZ. Sel. math., New ser. (2000) 6: 225. doi:10.1007/PL00001389


We prove a generalized rationality property and a new identity that we call the ''Jacobi identity'' for intertwining operator algebras. Most of the main properties of genus-zero conformal field theories, including the main properties of vertex operator algebras, modules, intertwining operators, Verlinde algebras, and fusing and braiding matrices, are incorporated into this identity. Together with associativity and commutativity for intertwining operators proved by the author in [H4] and [H6], the results of the present paper solve completely the problem of finding a natural purely algebraic structure on the direct sum of all inequivalent irreducible modules for a suitable vertex operator algebra. Two equivalent definitions of intertwining operator algebra in terms of this Jacobi identity are given.

Key words. Interwining operator algebras, generalized rationality, Jacobi identity 

Copyright information

© Birkhäuser Verlag, Basel 2000

Authors and Affiliations

  • Y.-Z. Huang
    • 1
  1. 1.Department of Mathematics, Rutgers University, 110 Frelinghuysen Rd., Piscataway, NJ 08854-8019, USA, e-mail: yzhuang@math.rutgers.eduUS

Personalised recommendations