Representational Theory of Infinite Dimensional Lie (super) Algebras and Related Algebraic Structures

无限维李（超）代数及相关代数结构的表示论

• 批准号: 0201017
• 负责人: Victor Kac
• 金额: $ 27.04万
• 依托单位: Massachusetts Institute of Technology
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2002
• 资助国家: 美国
• 起止时间: 2002-07-01 至 2006-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0201017&HistoricalAwards=false
• 关键词: Representational; Theory; Infinite; Dimensional; Lie

The project is concentrated around the following topics:1.Conformal superalgebra encodes an axiomatic description of theoperator product expansion in conformal field theory. 2.Representation theory of finite Lie pseudoalgebras. The nextgoal is representation theory of finite simple Liepseudoalgebras and the corresponding cohomology theory. 3.Representation theory of linearly compact Lie superalgebras and the Standard Model. The next challenge is to build their representationtheory. 4.Integrable representations of affine superalgebrasand near modular functions.This is a proposal in the area of mathematics known as Lie Algebras. Lie algebras are one of the tools mathematicians use to study all kinds of symmetries that occur in nature. In recent years, infinite-dimensional Lie algebras have been used to describe the symmetries of subatomic particles. The main objective of the project is to explore connections of the theory of infinite-dimensional symmetries to other fields of mathematics and to theoretical physics. It is hoped that this will lead to a better understanding of the structure of quarks and leptons

本课题主要围绕以下几个方面展开：1.共形超代数是对共形场理论中算符乘积展开的一种公理描述。2.有限李伪代数的表示理论。下一个目标是有限单李伪代数的表示理论和相应的上同调理论。3.线性紧李超代数的表示理论和标准模型。下一个挑战是建立他们的代表性理论。4.仿射超代数和拟模函数的可积表示。这是数学领域中的一个建议，称为李代数。李代数是数学家用来研究自然界中各种对称性的工具之一。近年来，无限维李代数被用来描述亚原子粒子的对称性。该项目的主要目标是探索无限维对称理论与其他数学领域和理论物理的联系。希望这将有助于更好地理解夸克和轻子的结构