Symmetry via braiding, diagrammatics and cellularity

通过编织、图表和细胞结构实现对称

• 批准号: DP150104507
• 负责人: Prof Gustav Lehrer
• 金额: $ 45.21万
• 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: 2015-07-01 至 2022-04-30
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP150104507
• 关键词: Symmetry; via; braiding; diagrammatics; cellularity

Symmetry is a basic organising tool for humans to understand their environment. Invariants are the mathematical embodiment of symmetry, and their study is as ancient as thought itself. This project aims to use the tools of braided tensor categories and cellular structure, to analyse the invariants occurring in several fundamental areas of mathematics, particularly relating to physics. The endomorphism algebras in certain tensor categories, particularly those for quantised superalgebras, will be realised as diagram algebras, and analysed using cellular theory. The intended output include criteria for semisimplicity, a new theory of diagram algebras, and decomposition theory which are expected to permit the determination of multiplicities of composition factors.

对称性是人类理解环境的基本组织工具。不变量是对称性的数学体现，对它们的研究和思想本身一样古老。该项目旨在使用编织张量范畴和细胞结构的工具，分析数学的几个基本领域中发生的不变量，特别是与物理学有关的不变量。某些张量范畴中的自同态代数，特别是量子化超代数，将被实现为图代数，并使用细胞理论进行分析。预期的输出包括标准半简单性，一个新的理论图代数，分解理论，预计将允许确定的多重组成因素。