Classical and affine W-algebras

经典和仿射 W 代数

• 批准号: DP150100789
• 负责人: Prof Alexander Molev
• 金额: $ 24.37万
• 依托单位: The University of Sydney
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2015
• 资助国家: 澳大利亚
• 起止时间: 2015-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP150100789
• 关键词: Classical; affine; algebras

The project aims to address major mathematical problems on representations of the families of quantum groups and vertex algebras associated with Lie algebras. It aims to create new connections between representation theory and mathematical physics. The theory of quantum groups originated from solvable lattice models in statistical mechanics and has turned out to have important connections with and applications to a wide range of subjects in mathematics and physics. The project aims to rely on these connections to extend and develop explicit theory of both the classical and quantum versions of the vertex algebras which are of great importance to conformal field theory and soliton spin chain models.

该项目旨在解决与李代数相关的量子群和顶点代数家族表示的主要数学问题。它的目的是在表示论和数学物理之间建立新的联系。量子群理论起源于统计力学中的可解格模型，并已被证明与数学和物理学中的广泛学科有重要联系和应用。该项目的目的是依靠这些连接扩展和发展显式理论的经典和量子版本的顶点代数是非常重要的共形场理论和孤子自旋链模型。