Cohomology and Representation Theory: Algebraic Groups, Finite Groups and Lie Algebras

9800960 Nakano该奖项支持在代数群及其相关结构的表示和上同调理论问题上的工作。这些相关结构包括李代数、无穷小群方案、量子群、Schur代数、对称群和Hecke代数。许多问题归结为研究某些有限维代数的表示理论。这些代数一般不是半单的，因此基本表示问题涉及确定单模和投射模、计算投射模的合成因子、理解块论和对不可分解模进行分类。首席研究员还将致力于几何方法在这些相关结构的表示/上同调理论中的使用。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。这项工作对数学的许多领域都有影响，包括环论、群论、拓扑学和李代数的研究。

9800960 Nakano This award supports work on problems in the representation and cohomology theory of algebraic groups and related structures. These related structures include Lie algebras, infinitesimal group schemes, quantum groups, Schur algebras, symmetric groups and Hecke algebras. Many of the problems reduce to studying the representation theory for certain finite-dimensional algebras. These algebras are in general not semisimple so the fundamental representation questions involve determining the simple and projective modules, computing the composition factors of the projective modules, understanding the block theory and classifying the indecomposable modules. The principal investigator will also work on the use of geometric methods in the representation/cohomology theory for these related structures. 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 implications for a number of areas of mathematics including ring theory, group theory, topology and the study of Lie algebras.