Affordable Access

Publisher Website

On the concepts of intertwining operator and tensor product module in vertex operator algebra theory

Authors
Journal
Journal of Pure and Applied Algebra
0022-4049
Publisher
Elsevier
Publication Date
Volume
204
Issue
3
Identifiers
DOI: 10.1016/j.jpaa.2005.05.005
Disciplines
  • Mathematics

Abstract

Abstract We produce counterexamples to show that in the definition of the notion of intertwining operator for modules for a vertex operator algebra, the commutator formula cannot in general be used as a replacement axiom for the Jacobi identity. We further give a sufficient condition for the commutator formula to imply the Jacobi identity in this definition. Using these results we illuminate the crucial role of the condition called the “compatibility condition” in the construction of the tensor product module in vertex operator algebra theory, as carried out in work of Huang and Lepowsky. In particular, we prove by means of suitable counterexamples that the compatibility condition was indeed needed in this theory.

There are no comments yet on this publication. Be the first to share your thoughts.