UTA Department of Mathematics

Mathematics and Statistics Colloquium

Date/Time/Room: Friday (10/13/2006) at 2:30pm in 304 Pickard Hall

Speaker: Dr. David J. Saltman, Mildred Caldwell and Baine Perkins Kerr Centennial Professor
Department of Mathematics, The University of Texas at Austin

"Division Algebras"

Abstract: On a bridge in Dublin in 1843, Hamilton is supposed to have carved ``i^2 = j^2 = k^2 = ijk = -1$'' which defines, over the reals, the so called algebra of quaternions, H. This algebra H is a sort of ``noncommutative'' field, where every nonzero element has an inverse but, in general, xy does not equal yx. Furthermore, as a vector space, H is finite dimensional (in fact 4 dimensional). By definition, this makes H a _division algebra_. The problem behind this talk is the question of finding or describing all division algebras. We will discuss what this means, and survey some of the results in this area. A theme we will emphasize is that the problem is concrete, but the tools one can use to study it are remarkably diverse.