Algebras with Frobenius morphisms and quantum groups

具有 Frobenius 态射和量子群的代数

• 批准号: DP0665124
• 负责人: Prof Jie Du
• 金额: $ 14.54万
• 依托单位: The University of New South Wales
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2006
• 资助国家: 澳大利亚
• 起止时间: 2006-01-01 至 2009-06-25
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP0665124
• 关键词: Algebras; Frobenius; morphisms; quantum; groups

In this digitalized world, our life relies on mathematics more than ever. Counting and numbers are just one example of this. Another is the public key codes for online payments and transactions. Mathematics is of enormous importance in this technology dominated age. This proposal is to carry out high level mathematical research in Australia. Basic research on quantum groups underpins applied research and certain areas such as quantum mechanics and string theory. Some structure of quantum groups is too complicated to be seen by even a professional mathematician. A possible interpretation by using representations over a finite field would make it more usable and accessible by computer.

在这个数字化的世界里，我们的生活比以往任何时候都更加依赖数学。计数和数字只是其中的一个例子。另一个是用于在线支付和交易的公钥代码。在这个技术主导的时代，数学是非常重要的。本课题拟在澳大利亚开展高水平的数学研究。量子群的基础研究是应用研究和某些领域如量子力学和弦理论的基础。量子群的一些结构过于复杂，甚至连专业数学家也看不出来。在有限域上使用表示法的可能解释将使计算机更易于使用和访问。