Abstract.
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.
We’re sorry, something doesn't seem to be working properly.
Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Huang, YZ. Generalized rationality and a ''Jacobi identity'' for intertwining operator algebras. Sel. math., New ser. 6, 225 (2000). https://doi.org/10.1007/PL00001389
DOI: https://doi.org/10.1007/PL00001389