Mathematical Sciences: Invariants and Trace Identities

该奖项涉及具有迹函数的代数及其迹恒等式的研究。特别感兴趣的是相关的泛代数和它们的Poincare级数。不变量理论将是一个重要的工具。主要研究人员感兴趣的是确定为什么有那么多具有迹的泛多项式恒等式代数作为重要群、李代数和超李代数的固定环出现。本研究属于环论的一般领域。环是定义了加法和乘法的代数对象。虽然加法运算满足交换律，但乘法运算不是必须的。乘法不可交换的环的一个例子是整数上的n×n矩阵的集合。非对易环的研究已经成为代数的重要组成部分，因为它对数学和物理的其他分支的意义越来越大。

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.