Infinite dimensional algebras and pro-p groups

我们计划研究泛线性pro-p群，即由一般矩阵生成的pro-p群。目的是利用pi代数理论的最新进展来证明某些相对言语宽度是有限的。这意味着自由的pro-p群和gold - shafarevich群都不是线性的。预期的结果将影响代数的几个分支，并阐明在代数数论中非常突出的无限代数对象。PI打算让他目前指导的三名研究生参与该项目的工作。

We plan to study universal linear pro-p groups, that is pro-p groups generated by generic matrices. The aim is to use recent advances in the theory of PI-algebras to show that certain relative verbal widths are finite. This will imply that free pro-p groups, and hence Golod-Shafarevich groups, are not linear.The expected results will affect several branches of Algebra and shed light on infinite algebraic objects that feature quite prominently in Algebraic Number Theory. The PI intends to involve three graduate students that he currently advises in the work on the project.