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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 $mathbb{N}$-graded modules by explicitly determining their Zhu algebras and show that these vertex algebras have only finitely many irreducible $mathbb{N}$-graded modules and they are $C_2$-cofinite.
In this paper we study the first cohomologies for the following three examples of vertex operator algebras: (i) the simple affine VOA associated to a simple Lie algebra with positive integral level; (ii) the Virasoro VOA corresponding to minimal mode
In this paper, we study a certain deformation $D$ of the Virasoro algebra that was introduced and called $q$-Virasoro algebra by Nigro,in the context of vertex algebras. Among the main results, we prove that for any complex number $ell$, the category
In this paper, we study nullity-2 toroidal extended affine Lie algebras in the context of vertex algebras and their $phi$-coordinated modules. Among the main results, we introduce a variant of toroidal extended affine Lie algebras, associate vert
In this paper we study the integral form of the lattice vertex algebra $V_L$. Based on the lattice structure, we introduce and study the associated modular vertex algebras $V_p$ and the quotient algebra $overline{V}_p$ as well as their irreducible mo
For any nullity $2$ extended affine Lie algebra $mathcal{E}$ of maximal type and $ellinmathbb{C}$, we prove that there exist a vertex algebra $V_{mathcal{E}}(ell)$ and an automorphism group $G$ of $V_{mathcal{E}}(ell)$ equipped with a linear characte