Twisted Forms of Differential Lie Algebras over $${\mathbb {C}}(t)$$ Associated with Complex Simple Lie Algebras

Abstract

Discussed here is descent theory in the differential context where everything is equipped with a differential operator. To answer a question personally posed by A. Pianzola, we determine all twisted forms of the differential Lie algebras over $${\mathbb {C}}(t)$$ associated with complex simple Lie algebras. Hopf–Galois Theory, a ring-theoretic counterpart of theory of torsors for group schemes, plays a role when we grasp the above-mentioned twisted forms from torsors.