Primitive Lie algebras of rational vector fields

TL;DR

This paper investigates the structure of transitive Lie algebras of rational vector fields on projective manifolds, linking them to algebraic homogeneous spaces and Lie algebra embeddings.

Contribution

It characterizes primitive Lie algebras of rational vector fields by associating them with rational maps to homogeneous spaces, revealing their algebraic structure.

Findings

Transitive Lie algebras correspond to rational maps to homogeneous spaces.

Primitive Lie algebras do not preserve any foliation.

The Lie algebra g maps into lie(G) via the rational map.

Abstract

A transitive Lie algebra g of rational vector fields on a projective manifold which do not preserve any foliation determines a rational map to an algebraic homogenous space G/H which maps g to lie(G).