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A realisation of the Bershadsky–Polyakov algebras and their relaxed modules

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 sl(2) and osp(1|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).

Vertex operator algebras ; W-algebras ; Lattice vertex algebras ; Relaxed highest-weight modules

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