A QUATERNIONIC CONSTRUCTION OF E7

We give an explicit construction of the simply-connected compact real form of the Lie group of type E-7, as a group of 28 x 28 matrices over quaternions, acting on a 28-dimensional left quaternion vector space. This leads to a description of the simply-connected split real form, acting on a 56-dimensional real vector space, and thence to the finite quasi-simple groups of type E-7. The sign problems usually associated with constructing exceptional Lie groups are almost entirely absent from this approach.