Mathematical Sciences: The Polynomial Identities and Invariants of nxn Matrices

9401266本研究涉及域上的nxn矩阵。主要讨论了n×n矩阵的多项式恒等式和不变量。关于一般矩阵环及其中心的问题，以及关于矩阵及其恒等式的组合问题，都是长期未解决的问题。第二个重点是某些无限群的nxn矩阵表示，特别是辫子群。这项研究支持矩阵理论、环理论和不变量的计算。特别是，这涉及到一个老问题，即确定在各种变换下保留哪些数学函数。这在许多科学领域和数学领域都很有趣。***

9401266 This research is concerned with nxn matrices over a field. The main focus is on the polynomial identities and invariants of nxn matrices. There are longstanding open problems about the ring of generic matrices and its center, as well as combinatorial problems about matrices and their identities. A secondary focus is on the nxn matrix representations of certain infinite groups, particularly the braid groups. The research supported concerns matrix theory, ring theory and the calculation of invariants. In particular, this involves an old problem of determining what mathematical functions are preserved under various transformations. This is of interest in many areas of science as well as in mathematics. ***