Irreducible weight and non-weight representations of some Lie algebras

一些李代数的不可约权重和非权重表示

• 批准号: RGPIN-2015-05813
• 负责人: Zhao, Kaiming
• 金额: $ 1.02万
• 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: 2018
• 资助国家: 加拿大
• 起止时间: 2018-01-01 至 2019-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=669771
• 关键词: Irreducible; weight; non; representations; some

Lie algebra theory has become more and more widely used in many branches of mathematics and physics, including, associative algebra, algebraic geometry, topology, differential geometry, differential equation, algebraic combinatorics, string theory, conformal field theory, soliton 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 problems for the theory and its applications. For example, one important problem is how to classify irreducible representations for various Lie algebras. The main objective of my research is to study some irreducible representations for important Lie algebras from physics (such as Kac-Moddy algebras, the Virasoro algebra, and the twisted Heisenberg-Virasoro algebra), and for other Lie algebras with useful structure (for example, super-elliptic Lie algebras, quantum torus Lie algebras and Witt algebras). Solutions to these problems will benefit theoretical studies in both physics and mathematics.**

Lie代数理论已在数学和物理学的许多分支中越来越广泛地使用，包括联想代数，代数几何，拓扑，拓扑，差异几何，微分等式，代数组合术，弦乐理论，共同场理论，孤子理论。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。它还为该理论及其应用提供了许多有趣的问题。例如，一个重要的问题是如何为各种代数分类不可还原表示。 The main objective of my research is to study some irreducible representations for important Lie algebras from physics (such as Kac-Moddy algebras, the Virasoro algebra, and the twisted Heisenberg-Virasoro algebra), and for other Lie algebras with useful structure (for example, super-elliptic Lie algebras, quantum torus Lie algebras and Witt algebras).解决这些问题的解决方案将受益于物理和数学的理论研究。**