Mathematical Sciences: PI Algebras in Prime Characteristics

这个项目涉及到应用模块化技术 对私家侦探的研究任意基域上的代数 特色 首席研究员将研究 PI的身份当 基本场的特征是零或正。 新 结果和技术联合收割机结合这两种情况， 上多项式的经典Procesi问题 在一般矩阵上的值可被p整除的整数。 本研究的主要工具是组合数学和群 表征理论 在这个项目中，代数的结构理论， 满足多项式恒等式将与应用一起检查 到组合数学和对称的表示理论 群和经典线性群。 一个代数的例子 满足多项式恒等式的环由以下环给出： 域上给定维数的矩阵。 事实上，这些往往 代数可以表示为矩阵的环。 这项工作 对几个不同领域的重要影响 数学

This project is concerned with applying modular techniques to the study of P.I. algebras over base fields of arbitrary characteristic. The principal investigator will study the identities of P.I. algebras in the various degrees when the characteristic of the base field is either zero or positive. New results and techniques combine these two cases and relate them to a classical problem of Procesi about polynomials over the integers whose values on generic matrices are divisible by p. The main tools in this study are combinatorics and group representation theory. In this project, the structure theory of algebras that satisfy polynomial identities will be examined with applications to combinatorics and the representation theory of the symmetric groups and the classical linear groups. An example of an algebra that satisfies a polynomial identity is given by the ring of matrices of a given dimension over a field. Indeed often these algebras can be represented as rings of matrices. This work has important consequences for several different areas of mathematics.