nxn Matrices - Representations of Infinite Groups and Invariants

福尔马内克 96-10118 这个项目有两个部分，都涉及域上的nxn矩阵。 第一部分是某些无限群的不可约n维表示的分类，如辫子群，映射类 群和Torelli群。 虽然目前还不可能 在所有维度中的完全分类，在低维度中的分类 应该是可能的。 请注意，数学家和物理学家已经构造了许多辫子群的表示，特别是与杨-巴克斯特方程有关的表示。 第二部分是研究n × n矩阵的不变量和恒等式。 这是环论和群论的研究， 代数 这些问题和攻击它们的方法是组合的，并且处理特定的环和群，而不是一般的理论。 如上所述，其中一些问题也是物理学家感兴趣的。

FORMANEK 96-10118 This project has two parts, both concerned with nxn matrices over a field. The first part is the classification of the irreducible n-dimensional representations of certain infinite groups, such as braid groups, mapping class groups, and Torelli groups. While there is presently no possibility of a complete classification in all dimensions, a classification in low dimensions should be possible. Note that many representations of braid groups have been constructed by both mathematicians and physicists, especially in connection with the Yang-Baxter equation. The second part is the study of the invariants and identities of nxn matrices. This is research in ring theory and group theory, two branches of algebra. The problems and methods to attack them are combinatorial, and deal with particular rings and groups, rather than general theory. As noted above, some of these questions are also of interest to physicists.