Division Algebras and Galois Groups

Document Type

Presentation Abstract

Presentation Date

3-26-1998

Abstract

A basic problem in algebra is to classify, for a given field K, the finite-dimensional division algebras having center K. The theorems of Frobenius and Wedderburn solve this problem in case K is the real field or a finite field. The classification for the rational field, or more generally an algebraic number field, was completed in the 1930s using deep results from algebraic number theory.

A finer study of the subfield structure of those algebras was initiated in the 1960s. Beginning with a polynomial f(x) with coefficients in K, one may ask whether there is a K-division algebra containing a root of f(x). The answer is known to depend on delicate properties of f(x) and K. In this talk I describe a few examples, and then discuss open questions and recent work concerning the Galois groups which arise in this manner.

Additional Details

Thursday, March 26, 1998
4:10 p.m. in MA 109
Coffee/Tea/Treats 3:30 p.m. in MA 104 (Lounge)

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