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