## EVENT DETAILS AND ABSTRACT

**Algebra Seminar**
**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 $F(M)^{S_{p}}$

**Date:** Tuesday, October 30, 2001

**Time:** 4:10pm

**Where:** Lunt 104

**Contact Person:** Prof. Matthew Emerton

**Contact email:** emerton@math.northwestern.edu

**Contact Phone:** 847-491-5544

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