An $S_3$-symmetry of the Jacobi Identity for Intertwining Operator Algebras

Abstract

We prove an $S_{3}$-symmetry of the Jacobi identity for intertwining operator algebras. Since this Jacobi identity involves the braiding and fusing isomorphisms satisfying the genus-zero Moore-Seiberg equations, our proof uses not only the basic properties of intertwining operators, but also the properties of braiding and fusing isomorphisms and the genus-zero Moore-Seiberg equations. Our proof depends heavily on the theory of multivalued analytic functions of several variables, especially the theory of analytic extensions.

37 pages, 2 figures. Several typos, including one in the key words, are corrected. Everything else is the same. The definition of intertwining operator algebras and the Jacobi identity in this paper are from arXiv:q-alg/9704008 by different author and arXiv:1503.06428. This definition and the statement of the Jacobi identity are long. They are the main text overlap with these two papers