**Authors:**Dražen Adamović, Ana Kontrec

Journal of Algebra and its applications (2020), https://doi.org/10.1142/S0219498821501024

**We study the representation theory of the Bershadsky-Polyakov algebra . In particular, Zhu algebra of is isomorphic to a certain quotient of the Smith algebra, after changing the Virasoro vector. We classify all modules in the category for the Bershadsky-Polyakov algebra for . In the case we show that the Zhu algebra has –dimensional indecomposable modules.**

**Abstract:****Keywords:**Vertex algebra, WW-algebras, Bershadsky–Polyakov algebra, Zhu’s algebra