论文标题
来自无限维谎言代数的顶点代数的统一结构
A unified construction of vertex algebras from infinite-dimensional Lie algebras
论文作者
论文摘要
在本文中，我们给出了由无限维谎言代数引起的顶点代数的统一结构，包括仿射Kac-Moody代数，Virasoro代数，Heisenberg代数及其较高的等级类似物，Orbifolds，Orbifolds和变形。我们定义了一个概念，即我们所谓的准顶点谎言代数来统一这些代数。从任何（最大）quasi顶点开始lie代数$ \ mathfrak {g} $，我们构造一个相应的顶点lie代数$ {\ mathfrak {\ mathfrak {g}} _ 0 $，并在受限的$ \ mathfrak $ distriant类别之间建立一个规范的同态性，并建立一个规范的同态。 $ v _ {\ mathfrak {g} _0} $ - 模块，其中$ v _ {\ mathfrak {g} _0} $是$ {\ mathfrak {g}}} _ 0 $的通用封装顶点代数。这使顶点代数的所有先前构建体从无限二的谎言代数和灯光上阐明，以将顶点代数与lie代数相关联。
In this paper, we give a unified construction of vertex algebras arising from infinite-dimensional Lie algebras, including the affine Kac-Moody algebras, Virasoro algebras, Heisenberg algebras and their higher rank analogs, orbifolds and deformations. We define a notion of what we call quasi vertex Lie algebra to unify these Lie algebras. Starting from any (maximal) quasi vertex Lie algebra $\mathfrak{g}$, we construct a corresponding vertex Lie algebra ${\mathfrak{g}}_0$, and establish a canonical isomorphism between the category of restricted $\mathfrak{g}$-modules and that of equivariant $ϕ$-coordinated quasi $V_{\mathfrak{g}_0}$-modules, where $V_{\mathfrak{g}_0}$ is the universal enveloping vertex algebra of ${\mathfrak{g}}_0$. This unified all the previous constructions of vertex algebras from infinite-dimensional Lie algebras and shed light on the way to associate vertex algebras with Lie algebras.
