2004/09/20 by Yi-Zhi Huang, Huang, Yi-Zhi, James Lepowsky +5
Mathematics · Physics and Astronomy · #17B69 #81T40 #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #hep-th #math-ph #math.MP #math.QA #msc:17B69 #msc:81T40
paper · pdf · doi:10.48550/arxiv.math/0409364
30 pages
arxiv created 2004/09/20 · arxiv updated 2009/12/01
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.