Mathematical Sciences: Invariants and Trace Identities

这个奖项是关于具有迹函数的代数及其迹恒等式的研究。特别有趣的是相关的泛代数和它们的庞加莱级数。不变量理论将是一个重要的工具。主要研究者感兴趣的是确定为什么那么多具有迹的普适多项式恒等式代数出现在重要群、李代数和超级李代数的固定环中。本研究属于环理论的一般范畴。环是一个代数对象，在它上面定义了加法和乘法。虽然加法运算满足交换律，但乘法运算不需要满足交换律。一个乘法不可交换的环的例子是整数上的nxn个矩阵的集合。非交换环的研究由于其对其他数学和物理分支的重要意义而成为代数的重要组成部分。

This award is concerned with the study of algebras with trace functions and their trace identities. Of special interest are associated universal algebras and their Poincare series. Invariant theory will be an important tool. The principal investigator is interested in determining why so many universal polynomial identity algebras with trace occur as fixed rings for important groups, Lie algebras and super Lie algebras. This research is in the general area of ring theory. A ring is an algebraic object having both an addition and a multiplication defined on it. Although the additive operation satisfies the commutative law, the multiplicative operation is not required to do so. An example of a ring for which multiplication is not commutative is the collection of nxn matrices over the integers. The study of noncommutative rings has become an important part of algebra because of its increasing significance to other branches of mathematics and physics.