Lie superalgebra representations: a geometric approach

李超代数表示：几何方法

• 批准号: DP220102530
• 负责人: A/Prof Artem Pulemotov
• 金额: $ 22.76万
• 依托单位: The University of Queensland
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2022
• 资助国家: 澳大利亚
• 起止时间: 2022-07-01 至 2025-06-30
• 项目状态: 未结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP220102530
• 关键词: Lie; superalgebra; representations; geometric; approach

The concept of a Lie group provides a mathematical underpinning for the idea of symmetry in mathematics, physics and chemistry. The project aims to advance two fundamental problems related to this concept: classification of unitary representations of Lie superalgebras, and the prescribed Ricci curvature problem on Lie groups. The research builds on newly-discovered connections between these problems to achieve exciting progress in their resolution. Outcomes are expected to find applications across a range of fields, such as condensed matter physics, particle physics, quantum field theory and knot theory. Anticipated benefits include stronger links between different areas of science achieved through a deeper understanding of symmetry.

李群的概念为数学、物理和化学中的对称性提供了数学基础。该项目旨在推进与此概念相关的两个基本问题：李超代数的酉表示的分类，以及李群上的规定Ricci曲率问题。这项研究建立在这些问题之间新发现的联系的基础上，以在解决这些问题方面取得令人兴奋的进展。预计成果将在一系列领域中得到应用，如凝聚态物理学，粒子物理学，量子场论和纽结理论。预期的好处包括通过对对称性的更深入理解，加强不同科学领域之间的联系。