Associating vertex algebras with the unitary Lie algebra

作者：Guo Hongyan; Wang Qing^*

来源：Journal of Algebra, 2015, 424: 126-146.

DOI：10.1016/j.jalgebra.2014.11.006

• Vertex algebras
• Unitary Lie algebra

In this paper, we associate vertex algebras and their two different kinds of module categories with the unitary Lie algebra (u) over cap (N)(C-(Gamma) over tilde) for N >= 2 being a positive integer and (Gamma) over tilde = {q(n) vertical bar n is an element of Z}, where the nonzero complex number q is not a root of unity. It is proved that for any complex number the category of restricted (u) over cap (N)(C-(Gamma) over tilde)-modules of level.e is canonically isomorphic to the category of quasi modules for certain vertex algebra. And we also prove that the category of restricted (u) over cap (N)(C-(Gamma) over tilde)-modules of level l is isomorphic to the category of Gamma-equivariant phi-coordinated quasi modules for the same vertex algebra, where Gamma is an automorphism group of this vertex algebra.

• 出版日期2015-2-15
• 单位厦门大学