Projective completions of Jordan pairs. Part I: The generalized projective geometry of a Lie algebra

TL;DR

This paper introduces a geometric framework for the projective completion of Jordan pairs linked to three-graded Lie algebras, laying the groundwork for manifold structures in future work.

Contribution

It provides a geometric realization of the projective completion of Jordan pairs associated with three-graded Lie algebras, enabling a structure theory development.

Findings

Geometric realization of projective completions for Jordan pairs

Foundation for manifold structures in subsequent research

Applicable over general base fields and rings

Abstract

A geometric realization of the projective completion of the Jordan pair corresponding to a three-graded Lie algebra is given which permits to develop a geometric structure theory of the projective completion. This will be used in Part II of this work to define a manifold structure on the projective completion (in arbitrary dimension and over quite general base fields and -rings).