Modular Representations of Finite Groups

Carlson，98-70035本课题是关于有限特征域上有限群的表示理论和上同调的研究。特别感兴趣的是强调基本模理论的表示的同调性质，以及作用于基本同调结构的群的上同调环的结构。该提出者计划继续开发用于模、同态和群上同调实验的计算机代数系统。群论领域是对称的数学理论，并与许多其他学科相互作用，例如数学之外的物理和化学、编码论、数论和数学内的几何。研究人员的特殊领域是表象理论、同调代数和计算机技术的使用。

CARLSON, 98-70035The project is an investigation into the representation theory and cohomology of finite groups over fields of finite characteristic. Of particular interest are the homological properties of representations which underline the basic module theory, and the structure of the cohomology ring of the group which acts on the fundamental homological constructions. The proposer plans to continue his development of computer algebra systems for experimentation with modules, homomorphisms and group cohomology.The field of group theory is the mathematical theory of symmetry and interacts with many other disciplines, for example physics and chemistry outside of mathematics, coding theory, number theory and geometry inside mathematics. The investigator's particular area is a meld of representation theory, homological algebra and the use of computer techniques.