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

Yi Zhi Huang, Y. Z. Huang

Research output: Contribution to journalArticlepeer-review

35 Scopus citations


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 conformai 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.

Original languageEnglish (US)
Pages (from-to)225-267
Number of pages43
JournalSelecta Mathematica, New Series
Issue number3
StatePublished - 2000

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Physics and Astronomy(all)


  • Generalized rationality
  • Interwining operator algebras
  • Jacob! identity


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