Mathematical Sciences: Cohomology and Representation Theory of Algebraic Groups and Lie Algebras

本课题主要研究代数群和李代数的表示理论。上同调环的光谱将是一个基本的感兴趣的对象。这将使主要研究者能够应用代数几何和代数拓扑学的方法来理解这些群和代数的表示/上同调理论。所支持的研究涉及各种代数对象的表示理论，包括代数群和李代数。表象理论是确定这些对象结构的重要方法。这项工作对环论、群论、拓扑学和李代数的研究等许多数学领域都有重要的意义。

This project is concerned with the representation theory of algebraic groups and Lie algebras. The spectrum of the cohomology ring will be a fundamental object of interest. This will enable the principal investigator to apply methods from algebraic geometry and algebraic topology in order to understand the representation/cohomology theory of these groups and algebras. The research supported concerns the representation theory of various algebraic objects including algebraic groups and Lie algebras. Representation theory is an important method for determining the structure of these objects. This work has important implications for a number of areas of mathematics including ring theory, group theory, topology and the study of Lie algebras.