We present a realisation of the universal/simple Bershadsky–Polyakov vertex algebras as subalgebras of the tensor product of the universal/simple Zamolodchikov vertex algebras and an isotropic lattice vertex algebra. This generalises the realisation of the universal/simple affine vertex algebras associated to \(\mathfrak {sl}_{2}\) and \(\mathfrak {osp} (1 \vert 2)\) given in Adamović (Commun Math Phys 366:1025–1067, 2019). Relaxed highest-weight modules are likewise constructed, conditions for their irreducibility are established, and their characters are explicitly computed, generalising the character formulae of Kawasetsu and Ridout (Commun Math Phys 368:627–663, 2019).

我们提出了通用/简单Bershadsky-Polyakov顶点代数的实现，作为通用/简单Zamolodchikov顶点代数和各向同性格子顶点代数的张量积的子代数。这概括了与Adamović（Commun Math Phys ）中给出的\（\ mathfrak {sl} _ {2} \）和\（\ mathfrak {osp}（1 \ vert 2）\）相关联的通用/简单仿射顶点代数的实现。366：1025-1067，2019）。同样构造轻松的最高权重模块，建立其不可约的条件，并明确计算它们的字符，从而概括了Kawasetsu和Ridout的字符公式（Commun Math Phys 368：627-663，2019）。