Mathematical Sciences: Homological Aspects of Representation Theory

该奖项支持的同源方面的研究， 代数的表示论特别是，校长 研究者将研究群环的上同调环， 有限维代数和分次代数。 他还将 研究了Hopf代数的结构和同调 字母-位置代数的子代数的性质， 在对称群的不变量理论中出现。 这 该项目还涉及继续发展一个象征性的 代数包的非交换环，将使用 广泛用于该研究项目。 这个项目是在非交换的一般领域 代数和计算机辅助计算方面， 领域 人们对使用计算机回答问题的兴趣越来越大 代数中的理论问题，反过来说，代数是相当 这对算法的开发很有用。 该项目使 认真运用象征主义的理论和实践 计算解决非交换代数中的真实的问题。

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.