论文标题
与顶点操作员代数相关的共同体学品种
Cohomological varieties associated to vertex operator algebras
论文作者
论文摘要
给定顶点操作员代数V，可以连接一个称为C2-Algebra R（V）的分级泊松代数。副泊松方案为V提供了重要的不变性，并已被Arakawa研究为相关的品种。在本文中，我们定义并检查了顶点代数的共同体学品种，这是与相关品种的共同体学偶数，该概念在顶点点衡量了相关方案的平滑度。我们研究其基本特性，然后构建共同体学品种的封闭子变量，用于由有限尺寸简单谎言代数构建的理性仿射算子代数。我们还确定了简单的Virasoro顶点操作员代数的共同体学品种。这些示例表明，尽管有理C2-磷酸根顶顶点操作员代数的相关品种始终是一个简单的点，但共同体的多样性可以具有尽可能大的尺寸。在本文中，我们仅将R（V）研究为可交换的代数，并且不使用其泊松结构的特性，该结构有望提供更精致的不变性。这项工作的目的是研究顶点代数的模块的共同体支持，作为有限群体的共同体支持品种和受限的LIE代数。
Given a vertex operator algebra V , one can attach a graded Poisson algebra called the C2-algebra R(V). The associate Poisson scheme provides an important invariant for V and has been studied by Arakawa as the associated variety. In this article, we define and examine the cohomological variety of a vertex algebra, a notion cohomologically dual to that of the associated variety, which measures the smoothness of the associated scheme at the vertex point. We study its basic properties and then construct a closed subvariety of the cohomological variety for rational affine vertex operator algebras constructed from finite dimensional simple Lie algebras. We also determine the cohomological varieties of the simple Virasoro vertex operator algebras. These examples indicate that, although the associated variety for a rational C2-cofinite vertex operator algebra is always a simple point, the cohomological variety can have as large a dimension as possible. In this paper, we study R(V) as a commutative algebra only and do not use the property of its Poisson structure, which is expected to provide more refined invariants. The goal of this work is to study the cohomological supports of modules for vertex algebras as the cohomological support varieties for finite groups and restricted Lie algebras.
