Logarithmic tensor category theory, VII: Convergence and extension properties and applications to expansion for intertwining maps

TL;DR

This paper advances tensor category theory for vertex operator algebras by establishing conditions for associativity isomorphisms, crucial for understanding the structure and applications of intertwining maps.

Contribution

It provides new sufficient conditions for the existence of associativity isomorphisms in tensor categories of vertex operator algebra modules.

Findings

Established conditions for associativity isomorphisms

Enhanced understanding of tensor category structure

Facilitated applications to intertwining map expansions

Abstract

This is the seventh 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 VII), we give sufficient conditions for the existence of the associativity isomorphisms.