EVENT DETAILS AND ABSTRACT

Title: Stable rationality of the center of the generic division ring
Speaker: Professor Esther Beneish
Speaker Info: Northwestern University
Brief Description:
Special Note:
Abstract:

Let F be an algebraically closed field, and let p be a prime. Let $C_{p}$ be the center of the division ring of $p\times p$ generic matrices over F. We show that $C_{p}$ is stably rational over F. The proof of this result can be briefly described as follows. Given a finite group G and a ZG-lattice M, $F(M)$ denotes the quotient field of the group algebra of the abelian group M. Procesi and Formanek have shown that the center $C_{p}$ is stably isomorphic to the fixed field under the action of the symmetric group, $S_{p}$, of $F(M)$ for a specific $ZS_{p}$-lattice M. We show that there is a central extension E of $S_{p}$ such that $F(ZE)^{E}$ is stably rational over F, and which is stably equivalent to $F(M)^{S_{p}}$