Embeddings and hyperplanes of the Lie incidence geometry of type E7,1

Abstract

This paper continues a program to show that for most of the standard Lie incidence geometries, all geometric hyperplanes arise from a necessarily absolutely universal embedding, by addingE7,1 to the list. It follows from [5, 12] that any projective embedding of this point line geometry is a homomorphic image of the one afforded by the 56-dimensional module for the groupE7(K).