Yang-Mills connections valued on the octonionic algebra
  We consider a formulation of Yang-Mills theory where the gauge field is valued on an octonionic algebra and the gauge transformation is the group of automorphisms of it. We show, under mild assumptions, that the only possible gauge formulations are the usual $\mathfrak{su}(2)$ or $\mathfrak{u}(1)$ Yang-Mills theories. 
A. Restuccia and J. P. Veiro
hep-th math-ph math.MP