AIMS Lie Groups: Fall-2022
Practice Exercises 12 : Due 12 Tue 20 Dec

1. Octonionic products I S0 4494S The commutator of two octonions \(p,q\in\mathbb{O}\) is defined by \[ [p,q] = pq - qp \] and the associator of three octonions \(p,q,r\in\mathbb{O}\) is defined by \[ [p,q,r] = (pq)r - p(qr) . \]
   1. Compute \([1+2i,2+3i+5j]\).
   2. Compute \([1+2i,2+3i+5j,7\ell]\).