Quantum algebras with supersymmetries

具有超对称性的量子代数

• 批准号: DP240101572
• 负责人: Prof Alexander Molev
• 金额: $ 26.97万
• 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: 2024
• 资助国家: 澳大利亚
• 起止时间: 2024-01-01 至 2026-12-31
• 项目状态: 未结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP240101572
• 关键词: Quantum; algebras; supersymmetries

The project aims to make fundamental advances in the theory of quantum algebras. It will develop explicit structure and representation theory of major classes of quantum algebras which are of great importance to quantum field theory and integrable models with supersymmetries. The intended outcomes include a solution of the outstanding classification problem for representations of quantum algebras with supersymmetries, which has remained open for the last two decades. It will involve newly-developed methods within the theory of quantum groups, and both the methods and classification will bring new mathematical instruments for the advance of supesymmetric conformal field theory and soliton spin chain models.

该项目的目标是在量子代数理论方面取得根本性进展。它会发展出明确的 结构和表示理论的主要类别的量子代数是非常重要的， 量子场论与超对称可积模型预期成果包括解决以下问题： 具有超对称性的量子代数表示的突出分类问题， 在过去的二十年里一直开放。它将涉及量子理论中新发展的方法 这两种方法和分类都将为促进数学的发展带来新的数学工具。 超对称共形场论和孤立子自旋链模型。