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A representation of the central extension of the unitary Lie algebra coordinated with a skew Laurent polynomial ring is constructed using vertex operators over an integral Z_2-lattice. The irreducible decomposition of the representation is explicitly computed and described. As a by-product, some fundamental representations of affine Kac-Moody Lie algebra of type $A_n^{(2)}$ are recovered by the new method.
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 $mathfrak{gl}_{infty}$
The aim of this paper is to introduce and study Lie algebras and Lie groups over noncommutative rings. For any Lie algebra $gg$ sitting inside an associative algebra $A$ and any associative algebra $FF$ we introduce and study the algebra $(gg,A)(FF)$
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, I investigate the ascending chain condition of right ideals in the case of vertex operator algebras satisfying a finiteness and/or a simplicity condition. Possible applications to the study of finiteness of orbifold VOAs is discussed.
We find sufficient conditions for the construction of vertex algebraic intertwining operators, among generalized Verma modules for an affine Lie algebra $hat{mathfrak{g}}$, from $mathfrak{g}$-module homomorphisms. When $mathfrak{g}=mathfrak{sl}_2$, t