论文标题
三角谎言代数，仿射kac-moody Lie代数和垂直级数模块用于顶点代数
Trigonometric Lie algebras, affine Kac-Moody Lie algebras, and equivariant quasi modules for vertex algebras
论文作者
论文摘要
在本文中，我们研究了一个无限维谎言代数$ \ widehat {x} _ {s} $的家庭，其中$ x $代表：$ a，b，c，c，d $和$ s $是一个亚伯集团，它概括了$ a，b，c，d $ d $ d $ d $ trigonometric liggementric Legebras。在主要结果中，我们确定$ \ wideHat {x} _ {s} $，所谓的仿射的协变代数为代数$ \ widehat {\ nathcal {l} _ {s} _ {s}} $，与某些自动性群体有关代数被视为谎言代数。然后，我们表明，限制的$ \ wideHat {x} _ {s} $ - 级别$ \ ell $的模块自然对应于extine vertex代数的epivariant准级模块，与$ \ nathcal {l} _ {s} $相关。此外，对于任何有限的循环组$ s $，我们完全确定了这四个Lie代数家族的结构，表明它们本质上是某些类型的Affine Kac-Moody Lie代数。
In this paper, we study a family of infinite-dimensional Lie algebras $\widehat{X}_{S}$, where $X$ stands for the type: $A,B,C,D$, and $S$ is an abelian group, which generalize the $A,B,C,D$ series of trigonometric Lie algebras. Among the main results, we identify $\widehat{X}_{S}$ with what are called the covariant algebras of the affine Lie algebra $\widehat{\mathcal{L}_{S}}$ with respect to some automorphism groups, where $\mathcal{L}_{S}$ is an explicitly defined associative algebra viewed as a Lie algebra. We then show that restricted $\widehat{X}_{S}$-modules of level $\ell$ naturally correspond to equivariant quasi modules for affine vertex algebras related to $\mathcal{L}_{S}$. Furthermore, for any finite cyclic group $S$, we completely determine the structures of these four families of Lie algebras, showing that they are essentially affine Kac-Moody Lie algebras of certain types.
