On a space related to the affine building of type E7

TL;DR

This paper investigates a special geometric structure related to the affine E7 building, constructing a covering space that reveals new insights into its algebraic and geometric properties.

Contribution

It introduces a new covering construction for a parapolar space of type A_{7,4} with an extra axiom, linking it to truncated affine E7 buildings.

Findings

Constructed a covering space that is a rank 6, residually connected, locally truncated diagram geometry.

Proved the covering space is a homomorphic image of a truncated affine E7 building.

Established that the original parapolar space is also a homomorphic image of a truncated building.

Abstract

A locally truncated geometry with diagram of type affine E7 is studied. One considers a parapolar space, locally of type A_{7,4}, which is subject to an extra axiom. A covering of this space is constructed; it is proved that this covering space is a rank 6, residually connected, locally truncated diagram geometry which is a homomorphic image of a truncated building of affine type E7. Consequently, the initial parapolar space is also a homomorphic image of a truncated building.