Logarithmic tensor category theory, VI: Expansion condition, associativity of logarithmic intertwining operators, and the associativity isomorphisms

2010/12/19 by Huang, Yi-Zhi, Lepowsky, James, Zhang, Lin · 2 citations
#17B69 #18D10 #81T40 #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1012.4202

Abstract

This is the sixth part in a series of papers in which we introduce and develop a natural, general tensor category theory for suitable module categories for a vertex (operator) algebra. In this paper (Part VI), we construct the appropriate natural associativity isomorphisms between triple tensor product functors. In fact, we establish a "logarithmic operator product expansion" theorem for logarithmic intertwining operators. In this part, a great deal of analytic reasoning is needed; the statements of the main theorems themselves involve convergence assertions.

Cited by

• Differential equations for intertwining operators among untwisted and twisted modules
• C₁-cofiniteness and vertex tensor categories

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