2005/06/01 by Yi-Zhi Huang, YI-ZHI HUANG · 4 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Current algebra #Differential operator #Discrete mathematics #Graph #Iterated function #Mathematical analysis #Mathematics #Nonlinear Waves and Solitons #Operator (biology) #Operator algebra #Pure mathematics #Tensor (intrinsic definition) #Tensor product #Vertex (graph theory) #Vertex operator algebra
paper · doi:10.1142/s0219199705001799
crossref issued 2005/06/01 · crossref published 2005/06/01 · crossref published-print 2005/06/01 · openalex publication_date 2005/06/01 · crossref created 2005/06/22 · crossref published-online 2011/11/20 · crossref deposited 2019/08/07 · openalex created_date 2025/10/10 · crossref indexed 2026/08/04 · openalex updated_date 2026/08/05
We show that if every module W for a vertex operator algebra V = ∐ n∈ℤ V (n) satisfies the condition dim W/C 1 (W)<∞, where C 1 (W) is the subspace of W spanned by elements of the form u -1 w for u ∈ V + = ∐ n>0 V (n) and w ∈ W, then matrix elements of products and iterates of intertwining operators satisfy certain systems of differential equations. Moreover, for prescribed singular points, there exist such systems of differential equations such that the prescribed singular points are regular. The finiteness of the fusion rules is an immediate consequence of a result used to establish the existence of such systems. Using these systems of differential equations and some additional reductivity conditions, we prove that products of intertwining operators for V satisfy the convergence and extension property needed in the tensor product theory for V-modules. Consequently, when a vertex operator algebra V satisfies all the conditions mentioned above, we obtain a natural structure of vertex tensor category (consequently braided tensor category) on the category of V-modules and a natural structure of intertwining operator algebra on the direct sum of all (inequivalent) irreducible V-modules.