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 c...
