ﻻ يوجد ملخص باللغة العربية
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 of restricted $D$-modules of level $ell$ is canonically isomorphic to the category of quasi modules for a certain vertex algebra of affine type. We also prove that the category of restricted $D$-modules of level $ell$ is canonically isomorphic to the category of $mathbb{Z}$-equivariant $phi$-coordinated quasi modules for the same vertex algebra. In the process, we introduce and employ a certain infinite dimensional Lie algebra which is defined in terms of generators and relations and then identified explicitly with a subalgebra of $mathfrak{gl}_{infty}$.
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 $p$-
In this paper, we explore a canonical connection between the algebra of $q$-difference operators $widetilde{V}_{q}$, affine Lie algebra and affine vertex algebras associated to certain subalgebra $mathcal{A}$ of the Lie algebra $mathfrak{gl}_{infty}$
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
We first determine the automorphism group of the twisted Heisenberg-Virasoro vertex operator algebra $V_{mathcal{L}}(ell_{123},0)$.Then, for any integer $t>1$, we introduce a new Lie algebra $mathcal{L}_{t}$, and show that $sigma_{t}$-twisted $V_{mat
We find that a compatible graded left-symmetric algebra structure on the Witt algebra induces an indecomposable module of the Witt algebra with 1-dimensional weight spaces by its left multiplication operators. From the classification of such modules