EVENT DETAILS AND ABSTRACT

Title: Annihilators in Cayley-Dickson algebras
Speaker: Professor Daniel Biss
Speaker Info: University of Chicago
Brief Description:
Special Note:
Abstract:

The Cayley-Dickson algebras form a sequence of R-algebras beginning with the real numbers, the complex numbers, the quaternions, and the octonions. We rarely hear about the subsequent members of this sequence, since they not only lack associativity but also have zero-divisors (as the Hopf invariant 1 theorem demands). These zero-divisors, however, can be viewed not as a pathology but rather as an opportunity; the zero-divisors in the 16-dimensional Cayley-Dickson algebra give rise to the Lie group G_2, and in the larger algebras they seem to be even more interesting. We'll describe joint results with Dan Dugger and Dan Isaksen about the geometry of these spaces of zero-divisors.