Vertex algebras associated to abelian current algebras

Abstract

We construct a family of vertex algebras associated to the current algebra of finite-dimensional abelian Lie algebras along with their modules and logarithmic modules. We show this family of vertex algebras and their modules are quasi-conformal and strongly $\mathbb{N}$-graded and verify convergence and extension property needed in the logarithmic tensor category theory for strongly graded logarithmic modules developed by Huang, Lepowsky and Zhang.

24 pages, Comments are very welcome. arXiv admin note: text overlap with arXiv:math/0206206, arXiv:1012.4193 by other authors

References in corpus (3)

• Current algebras, highest weight categories and quivers
• Tensor products of strongly graded vertex algebras and their modules
• Differential equations and logarithmic intertwining operators for strongly graded vertex algebras