engleski

Classification of irreducible modules for Bershadsky–Polyakov algebra at certain levels

We study the representation theory of the Bershadsky–Polyakov algebra W_k=W_k(sl_3, f_θ). In particular, Zhu algebra of Wk is isomorphic to a certain quotient of the Smith algebra, after changing the Virasoro vector. We classify all modules in the category O for the Bershadsky– Polyakov algebra W_k for k=−5/3, −9/4, −1, 0. In the case k=0, we show that the Zhu algebra A(W_k) has two-dimensional indecomposable modules.

Vertex algebra ; W-algebras ; Bershadsky–Polyakov algebra ; Zhu’s algebra

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