13 March 2018
2:30 - 3:30   Michael Barr (McGill)
On Peter Freyd's substantial simplification of Frobenius's theorem on finite dimensional real division algebras.

Abstract: A well-known theorem of Frobenius states that a finite dimensional real division algebra is either the reals, complex numbers, or the quaternions. The standard proofs are fairly complicated (see Wikipedia for example). By a clever use of conjugation, Peter reduced the result to a simple argument that is so pretty I would like to present it. I will also explain the centrality of centrality in the argument, why the result fails if the reals are not centrally embedded in the algebra, which goes back to Gerstenhaber and Fine in my student days.