Max Chemtov, Department of Pure Mathematics, University of Waterloo
"Subalgebras of so(7) Induced by the Coassociative 4-Form on R^7"
Consider the 2-forms on R^7 resulting from evaluating the coassociative 4-form on two vectors. It turns out that, when such vectors are restricted to an associative 3-plane P, these 2-forms along with those in Λ^2(P) give a subalgebra of so(7) isomorphic to so(3) ♁ so(3). After giving some brief context, we will discuss this fact and characterize the intersections of such subalgebras for different choices of P.