Mathematical Sciences: Invariants and Trace Identities

这个奖项是关于代数的研究， 跟踪函数及其跟踪恒等式。 特别关注的 是关联的泛代数及其庞加莱级数。 不变量理论将是一个重要的工具。 校长 调查人员有兴趣确定为什么这么多普遍的 有迹多项式单位代数作为不动环出现， 重要群、李代数和超李代数。 这项研究是在环理论的一般领域。 的环 是一个既有加法又有 乘法定义。虽然加法运算 满足交换律，乘法运算是 不需要这样做。 一个环的例子， 乘法不是交换的是nxn的集合 整数上的矩阵。 非交换环的研究 已经成为代数的一个重要组成部分，因为它的增长 对数学和物理学的其他分支具有重要意义。

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.