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Mathematical Sciences: Lie Algebras, Lie Superalgebras, and Quantum Groups

数学科学：李代数、李超代数和量子群

基本信息

批准号：
9207701
负责人：
Richard Block
金额：
$ 10.04万
依托单位：
University of California-Riverside
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
1992
资助国家：
美国
起止时间：
1992-07-01 至 1996-06-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=9207701&HistoricalAwards=false
关键词：
Mathematical Sciences Lie Algebras Superalgebras

项目摘要

This award concerns research on the theory of Lie algebras. One of the principal investigators will work on the classification of simple and semisimple Lie superalgebras of prime characteristic. He will also work on vertex operators, specifically on explicit construction of certain modules, as well as on certain Hopf algebras. A second principal investigator will study representations of quantum groups and associated solutions of the quantum Yang-Baxter equations. She plans work on the case of quantum enveloping algebras of affine Kac-Moody Lie algebras at roots of unity. She also plans to describe minimal cyclic representations, and in particular to show that the minimum dimension equals the dimension of the minimal orbit of the corresponding Lie group. A third principal investigator will study various aspects of the representation theory of Lie superalgebras. He will work on generic modules over classical Lie superalgebras and twisted D-modules; finite-dimensional atypical modules of classical Lie superalgebras; representations of Cartan-type classical Lie superalgebras; representations of semisimple Lie superalgebras; and representations of Kac-Moody Lie superalgebras. This research is concerned with a mathematical object called a Lie algebra. Lie algebras arise from another object called a Lie group. An example of a Lie group is the rotations of a sphere where one rotation is followed by another. Lie groups and Lie algebras are important in areas involving analysis of spherical motion.

该奖项涉及对谎言理论的研究代数其中一名主要调查员将研究的单和半单李超代数的分类主要特征他还将致力于顶点运营商，特别是某些模块的显式构造，以及在某些Hopf代数上。第二个首席研究员将研究量子群及其相关的表示量子杨-巴克斯特方程的解她计划工作关于仿射Kac-Moody量子包络代数单位根上的李代数。她还计划描述最小循环表示，特别是要表明，最小维数等于最小轨道的维数对应的Lie Group。第三位首席研究员我将研究Lie表示理论的各个方面超代数他将研究通用模块，而不是经典模块。李超代数与扭D-模;有限维经典李超代数的非典型模;表示 Cartan型经典李超代数; 半单李超代数及Kac-Moody表示李超代数这项研究涉及一个数学对象，李代数李代数起源于另一个叫做李群。李群的一个例子是一个一个旋转之后是另一个旋转的球体。李群和李代数在涉及以下分析的领域中是重要的：球面运动