Vertex Operator Algebras and Deformation Quantization of Poisson Algebras

顶点算子代数与泊松代数的变形量化

基本信息

批准号：
9970496
负责人：
Haisheng Li
金额：
$ 7.15万
依托单位：
Rutgers University New Brunswick
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
1999
资助国家：
美国
起止时间：
1999-09-01 至 2002-08-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=9970496&HistoricalAwards=false
关键词：
Vertex Operator Algebras Deformation Quantization

项目摘要

9970496To a vertex operator algebra V we associate a space PA(V)(a subspace of V) and define a product *_{h} depending on a formal parameter h on PA(V) in terms of vertex operators. It follows from some known results that PA(V) is a generating subspace of the vertex operator algebra V with a spanning property similar to the one in the classical PBW theorem and that PA(V) has a Poisson algebra structure. Our first goal is to prove that (PA(V),*_{h}) is a *-deformation of the Poisson algebra PA(V) and to prove that (PA(V),*_{h}) uniquely determines the vertex operator algebra structure on V. Our second goal is to prove that for a given abstract Poisson algebra P equipped with a *-deformation structure *_{h}satisfying a certain condition, there exists a vertex operator algebra V such that (PA(V),*_{h}) is isomorphic to (P,*_{h}). It is known that *-deformation has a geometric origin. So our third goal is for a vertex operator algebra V to use the above link to find a geometric object G(V) with a *-product structure, which is canonically related to (PA(V),*_{h}).These algebras arise from the study of quantum field theory in physics. Connections with other areas like number theory also exist. By determining the properties of these algebraic objects new insights into certain aspects of physics might be expected.

9970496至一个顶点操作员代数v我们将空间pa（v）（v）（v的子空间）关联，并根据顶点操作员在pa（v）上的正式参数h（v）定义产品 *_ {h}。从一些已知的结果来看，PA（V）是顶点操作员代数V的生成子空间，其子宫属性类似于经典PBW定理中的属性，并且PA（V）具有泊松代数结构。我们的第一个目标是证明（Pa（v）， *_ {h}）是Poisson代数PA（v）的 * - 形式，并证明（Pa（v）， *_ {h}）唯一地确定了Vertex Opertor algebra的结构，以证明我们的第二个目标是证明A poisson poisson poisson al al al al al albra Albra Albra Albra Albra Albra Albra Albra Albra Albra Albra Albra Albra Albra Albra Albra Albra Albra Albra al an al albra a al al albra *_ {h}满足某种条件，存在一个顶点操作员代数V，使得（Pa（v），*_ {H}）对（P，*_ {H}）是同构的。众所周知， *形式具有几何起源。因此，我们的第三个目标是使顶点操作员代数V使用上述链接以找到具有 * - 产品结构的几何对象G（V），该对象与（Pa（v）， *_ {h}）在规范上相关。这些代数来自物理学中量子现场理论的研究。与其他领域的联系也存在。数字理论也存在。通过确定这些代数对象的属性，可能会预期对物理某些方面的新见解。