Restricted modules and associated vertex algebras of extended Heisenberg-Virasoro algebra

作者：Guo, Hongyan^*; Li, Huaimin

来源：Journal of Algebra, 2023, 635: 463-485.

DOI：10.1016/j.jalgebra.2023.07.044

• algebra
• Restricted module
• Irreducible module
• Vertex algebra

In this paper, a family of infinite dimensional Lie algebras G & SIM; is introduced and investigated, called the extended Heisenberg-Virasoro algebra, denoted by G & SIM;. These Lie algebras are related to the N = 2 superconformal algebra and the Bershadsky-Polyakov algebra. We study restricted modules and associated vertex algebras of the Lie algebra G & SIM;. More precisely, we construct its associated vertex (operator) algebras VL & SIM;(e123, 0), and show that the category of vertex algebra VL & SIM;(?123, 0)-modules is equivalent to the category of restricted & SIM; of level & POUND;123. Then we give uniform constructions of simple restricted G & SIM;-modules. Also, we present several equivalent characterizations of simple restricted modules over G & SIM;.& COPY; 2023 Elsevier Inc.