Abstract
In this paper, we study Virasoro vertex algebras and affine vertex algebras over a general field of characteristic p>2. More specifically, we study certain quotients of the universal Virasoro and affine vertex algebras by ideals related to the p-centers of the Virasoro algebra and affine Lie algebras. Among the main results, we classify their irreducible N-graded modules by explicitly determining their Zhu algebras and show that these vertex algebras have only finitely many irreducible N-graded modules and they are C2-cofinite.
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