Mathematical Sciences: Polynomial Identities and Graded Identities

最近在PI代数的研究中引入了新的机制，这表明对Z/2Z-分次代数的研究可以得到关于PI代数恒等式的信息。本课题致力于研究这些代数，特别是它们的分次恒等式。本研究属于非对易环论的一般领域。特别地，它涉及到满足多项式方程的一类特殊的环。这个领域，随着组合定理的发现，提供了对代数结构理论的洞察，已经成为当前环论研究的一个令人兴奋的话题，对表示论和对称群有影响。

New machinery has recently been introduced into the study of PI algebras which show that the study of Z/2Z-graded algebras yields information about the identities of PI algebras. This project is concerned with investigating these algebras, especially their graded identities. This research is in the general area of noncommutative ring theory. In particular, it is concerned with a particular class of rings which satisfy a polynomial equation. This area, with the discovery of combinatorial theorems that provide insight into the structure theory of the algebra, has become an exciting topic of current research in ring theory with implications for representation theory and the symmetric group.