A LOGARITHMIC GENERALIZATION OF TENSOR PRODUCT THEORY FOR MODULES FOR A VERTEX OPERATOR ALGEBRA

2003/11/30 by Yi-Zhi Huang, YI-ZHI HUANG, James Lepowsky +3 · 41 citations
Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic structures and combinatorial models #Generalization #Homotopy and Cohomology in Algebraic Topology #Logarithm #Rings, Modules, and Algebras #Tensor (intrinsic definition) #Tensor product #Tensor product of algebras #Tensor product of modules #Vertex (graph theory) #hep-th #math.QA #math.RT #msc:17B69 #msc:18D10 #msc:81T40

paper · pdf · doi:10.1142/s0129167x06003758

published in International Journal of Mathematics 17(08), 975-1012 (World Scientific) · 39 pages. Misprints corrected. Final version

openalex publication_date 2006/09/01 · arxiv created 2006/09/28 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We describe a logarithmic tensor product theory for certain module categories for a "conformal vertex algebra". In this theory, which is a natural, although intricate, generalization of earlier work of Huang and Lepowsky, we do not require the module categories to be semisimple, and we accommodate modules with generalized weight spaces. The corresponding intertwining operators contain logarithms of the variables.

Citations

• BITS AND PIECES IN LOGARITHMIC CONFORMAL FIELD THEORY

Cited by

• RIGIDITY AND MODULARITY OF VERTEX TENSOR CATEGORIES
• Tensor categories of affine Lie algebras beyond admissible levels
• Coupling a vertex algebra to a large center