TY - JOUR

T1 - On the concepts of intertwining operator and tensor product module in vertex operator algebra theory

AU - Huang, Yi Zhi

AU - Lepowsky, James

AU - Li, Haisheng

AU - Zhang, Lin

N1 - Funding Information:
Y.-Z.H., J.L. and L.Z. gratefully acknowledge partial support from NSF grant DMS-0070800 and H.L. gratefully acknowledges partial support from an NSA grant.

PY - 2006/3

Y1 - 2006/3

N2 - 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.

AB - 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.

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U2 - 10.1016/j.jpaa.2005.05.005

DO - 10.1016/j.jpaa.2005.05.005

M3 - Article

AN - SCOPUS:29744450733

SN - 0022-4049

VL - 204

SP - 507

EP - 535

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

IS - 3

ER -