Mathematical Sciences: Homological Aspects of Representation Theory

该奖项支持对代数表示理论的同调方面的研究。特别是，主要研究者将研究群环、有限维代数和分次代数的上同调环。他还将研究Hopf代数的结构和在对称群不变理论中出现的字母位置代数的商的同调性质。这个项目还包括继续开发一个非对易环的符号代数程序包，该程序包将被广泛用于这一研究项目。这个项目是在非对易代数的一般领域和这一领域的计算机辅助计算方面。人们对使用计算机回答代数中的理论问题越来越感兴趣，相反，代数对算法的发展非常有用。这个项目认真利用符号计算的理论和实践来解决非对易代数中的实际问题。

This award supports the study of homological aspects of the representation theory of algebras. In particular, the principal investigator will study the cohomology ring of group rings, of finite dimensional algebras and of graded algebras. He will also study the structure of Hopf algebras and the homological properties of the quotients of the letter-place algebras which arise in the invariant theory of the symmetric groups. This project also involves the continued development a symbolic algebra package for noncommutative rings which will be used extensively for this research project. This project is in the general area of noncommutative algebra and the computer-aided computational aspects of this field. There is a growing interest in using computers to answer theoretical questions in algebra and conversely, algebra is quite useful for the development of algorithms. This project makes serious use of both the theory and practice of symbolic calculations to solve real problems in noncommutative algebra.