Logarithmic tensor category theory, IV: Constructions of tensor product bifunctors and the compatibility conditions

Abstract

This is the fourth 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 IV), we give constructions of the P(z)- and Q(z)-tensor product bifunctors using what we call "compatibility conditions" and certain other conditions.

Part IV of a series of 8 papers generalizing the results in and collectively replacing arXiv:0710:2687, with new titles. 94 pages. Minor changes