Modular Lie algebras and representation theory

模李代数和表示论

• 批准号: 2281585
• 金额: --
• 依托单位: University of Birmingham
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2019
• 资助国家: 英国
• 起止时间: 2019 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2281585
• 关键词: Modular; Lie; algebras; representation; theory

The project concerns the theory of Lie algebras over fields of positive characteristic. Given the Lie algebra of a reductive algebraic group, we will consider questions about subalgebras containing a given nilpotent element. A fundamental question is to determine the subalgebras isomorphic to the special linear Lie algebra, and we plan to make progress understanding such subalgebras for restricted nilpotent elements. Further investigation will be made in to the smallest simple restricted subalgebra containing a nonrestricted nilpotent element. Subsequently, we plan to make progress in understanding all semisimple subalgebras containing a nilpotent elements in large orbits.The methods will involve the representation theory of modular Lie algebras and cohomology of representations. In the case of groups of classical type, the natural representation and the theory of Jordan normal form will be employed, whereas computational methods may be used for the case of groups of exceptional type.EPSRC subject area: Algebra

该项目涉及积极特征领域的谎言代数理论。鉴于还原代数组的谎言代数，我们将考虑有关包含给定的nilpotent元件的亚代词的问题。一个基本问题是确定特殊线性谎言代数的亚代构象同构，我们计划使人们了解这种限制性nilpotent元素的亚代代代数。进一步研究将对包含不受限制的尼尔氏元件的最小简单限制的亚代词。随后，我们计划在理解大轨道中包含nilpotent元素的所有半神经子代理方面取得进展。该方法将涉及模块化代数代数的表示理论和表示形式的共同体。对于古典类型组，将采用自然代表和约旦正常形式的理论，而计算方法可以用于特殊类型组的情况下。EPSRC主题领域：代数