Weight representations of lie algebras

李代数的权重表示

• 批准号: 311907-2010
• 负责人: Zhao, Kaiming
• 金额: $ 1.53万
• 依托单位: Wilfrid Laurier University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2013
• 资助国家: 加拿大
• 起止时间: 2013-01-01 至 2014-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=526302
• 关键词: Weight; representations; lie; algebras

Lie algebra theory has become more and more widely used in many branches of mathematics, physics, and finance. Associative algebra theory, topology, differential geometry, algebraic combinatorics, theory of 2-dimensional statistical models, string theory, conformal field theory, soliton theory, and other mathematical physics all use Lie algebra theory. Besides being useful in many subjects, Lie algebra theory is inherently attractive, combining a great depth and a satisfying degree of completeness in its basic theory. It also presents many interesting and important problems. For example, how to classify various representations for different Lie algebras and find out their character formulas. The main objective of my research is to study good representations for some important Lie algebras from physics (such as Kac-Moddy algebras, generalized Virasoro algebras and the twisted Heisenberg-Virasoro algebra), and for some other Lie algebras with useful structure (for example, quantum torus Lie algebras and generalized Cartan type Lie algebras). Solutions to these problems will advance theoretical studies in both physics and mathematics.

谎言代数理论已在数学，物理和金融的许多分支中越来越广泛地使用。联想代数理论，拓扑，差异几何学，代数组合学，二维统计模型的理论，弦理论，保形场理论，孤子理论和其他数学物理学都使用了lie代数理论。除了在许多学科中有用外，谎言代数理论本质上具有吸引力，它的深度和令人满意的完整性与其基本理论相结合。它还提出了许多有趣且重要的问题。例如，如何对不同的代数分类分类并找出其性格公式。我的研究的主要目的是研究物理学的一些重要代数（例如Kac-Moddy代数，广义的Virasoro代数和Twisted Heisenberg-Virasoro代数），以及其他具有有用结构的lie代数（例如，Quantum lie algebras anderic contrical cartan类型）。解决这些问题的解决方案将推进物理和数学的理论研究。