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

该项目涉及的理论李代数领域的积极特征。给定约化代数群的李代数，我们将考虑包含给定幂零元的子代数的问题。一个基本的问题是确定同构的特殊线性李代数的子代数，我们计划取得进展，了解这样的子代数的限制幂零元素。进一步研究了含有非限制幂零元的最小单限制子代数。接下来，我们计划在理解所有在大轨道上包含幂零元的半单子代数方面取得进展，方法将涉及模李代数的表示理论和表示的上同调。在经典类型的群的情况下，将采用自然表示和约旦标准形理论，而计算方法可以用于例外类型的群的情况。EPSRC主题领域：代数